A resident of the Illawarra's northern suburbs, Do's painting depicts his father Tam emerging from the canvas in thick swathes of paint, his dark eyes staring intently at the viewer.

Artist Ben Quilty, one of 11 trustees of the Art Gallery of NSW who judge the prize, describes the portrait as a "lovely surprise".

"We didn't know it was Anh's work," Quilty says. "But there is an honesty and quiet strength in the painting that stood out immediately.''

The 37-year-old Do painted his father, who brought his family to Australia as refugees in 1980, shortly after a stay in hospital. The artist tells the story in the exhibition label: "He'd dropped to 50 kilos and when I hugged him I could feel his ribs. I spent the next few days wondering how long this skinny, fearless man could keep defying the odds."

"That's a son's painting of a dad that he worries he might not see again," says Do.

Beyond a son's concern for his ailing father, Do's portrait tells a more complicated story of Tam's alcoholism and abandonment of the family he rescued from strife-torn Vietnam.

Do has built an impressive comic career across television, stand-up and film; his sunny demeanour has featured on television programs including The Matty Johns Show, Pizza and his ongoing travelogue series Anh Does….

But that is a different side to the contemplative man reliving the turmoil caused by his father's addiction. "He drank heavily and when I was 13 he left the family," he says. "I didn't see him for eight years and I hated him for a big part of my childhood just for not being there and making mum look after three kids on six bucks an hour."

It wasn't until Do was 21 and studying law at the University of Technology, Sydney, that he decided to seek out his father, who was living in Melbourne. He recalls driving through the night for the reunion only to be confronted at the door of his father's unit by a woman, barely older than Do, with a baby.

"And I figure, 'Wow, I've got this half-brother'," Do says. "To find that out is confronting.

"I thought to myself, I won't hang around for long. But I'd driven from Sydney to Melbourne so I thought I'd have a quick bite and I'll walk away and never come back. Obviously he's moved on.

"'Dad', I said. 'He's cute. What's his name'?"

His father's reply: "Anh. I named him after you."

That revelation was a bombshell for Do after so many years of hating his father. "I thought my father had forgotten about me," he says. "But I realised that he missed me as much as I missed him."

Do is sitting upstairs in the coastal home he has made with wife Suzanne and their four children – three-month-old daughter Summer and her older brothers, five-year-old Leon, Luc, 8 and Xavier, 10. Downstairs in a double garage is his studio, impeccably neat and organised with military precision. Four large heads – created with thick swathes of paint lathered on canvas like frosting on a cake – sit on easels around a large table covered in paint-splattered plastic.

Neatly-stacked tubs are filled with chef's palette knives of varying length and lethalness. Do uses them to apply paint in quick, broad strokes. Stacks of heavy hardcover books about artists such as Rembrandt, Cy Twombly and Pete Doig fill one tabletop, while another is arranged with tins of oil paint. Light and the chill air seeps through sliding doors that look out on the ocean on this stormy winter's day.

Upstairs, Do's back is turned to the scenic vista of coastal cliffs and beach battered by furious seas as he reflects on his father. "Now that I have four kids, I realise you love your kids forever, no matter what," he says. "You love your kids forever."

Do admits his younger self found it difficult to understand his father's actions. "He used to call my grandma every week to check on us," he says. "And I said, 'Why didn't you come back?'

"And he said, 'You guys were doing so well without me. I didn't want to come back and have my drinking affect you guys'."

Do has rebuilt a relationship with his father, who he says is now "my best mate in the whole world".

"I realised when he's not intoxicated he's the best dad."

Do told the story of his relationship with his father and the family's arduous journey to Australia as boatpeople in his award-winning 2010 autobiography, The Happiest Refugee.

Painting a portrait of his father brought back those memories and the feelings he experienced during those years of estrangement. He worked on the portrait in his garage studio, painting with music in the background. Each song took him back to his younger days.

"I had some music on, it was just a mix, and then Nirvana comes on," he says. "And I remember being 14, nah about 16, listening to Nirvana, hating my dad and so I went through a period of painting where I was hating him."

But a new song triggered a different mood. "Some Leonard Cohen came on and that was when I reconnected with him," he says. "So I start crying, y'know, because that's when I saw him again."

Do says he also cried while writing about his father in The Happiest Refugee. "At least with painting it was all done in about four-and-a-half hours."

But there were no tears when Do took his father to the Art Gallery of NSW to see the portrait. "He looked at it and he goes, 'I reckon I look better than that'," Do says. "And then he said, 'Nah, that's me on a Saturday arvo after losing at the horses'."

Do's brother Khoa, a filmmaker and board member of the Australia Council for the Arts, says the portrait is "really very powerful".

"I think it captures the essence of our father exceptionally well – especially in those eyes," he says. "Eyes of such pain and longing mixed in with a quiet peace and acceptance."

The director of the Schapelle Corby telemovie, Khoa says his father's departure was unexpected and particularly tough on his older brother. "I remember a period of moving from one place to another, living in a sewing factory for a while, helping Mum make garments so she could pay for electricity bills," he says. "But I guess just as quickly as our father left, my brother, sister and I grew up."

In contrast to his flawed father, Do says his mother Hien was always supportive, even as she struggled to support her family single-handedly working three jobs. He recalls her buying second-hand books from an op shop when he was struggling with English. "Of course, it's not like her reading was any good but she was trying," Do says.

As a teenager, Do became the family's spokesman, calling landlords to ask for extra time to pay the rent. "It makes you grow up fast," he says.

Do turned his autobiography into a stage show that he will perform again around Australia in October and November, including dates at the State Theatre and Enmore Theatre in Sydney and the Canberra Theatre. He is also working on a film script based on The Happiest Refugee after Russell Crowe bought the movie rights for the book.

Do says he accepted Crowe's offer with one "absolute condition". "I really want to play the role of my father, and Russell said, 'Deal'," he says.

Do has also written three children's books including The Little Refugee, a retelling of his autobiography for young readers. Yet he shies away from commenting directly on debates about the treatment of refugees.

"I'm a comedian," he says. "It's like this. I'm an asthmatic so if you want to ask someone about asthma, ask a doctor. I'm asthmatic but I'm not an expert on it."

Do's fearless approach to life is nonetheless shaped by his experience as a refugee. He was always interested in art but studied law at university because he was determined to buy his mother a house. "We moved house 20-something times because of financial reasons," Do says. "I just didn't want a landlord to kick us out any more."

At the end of his law degree, he tried stand-up comedy, starting on the career that has brought him considerable success for more than a decade. Yet he says: "I think I got into the wrong job, you know, when I became a comedian. I prefer the company of my family or close friends. You don't see me going to a lot of events like the Logies and all that kind of stuff. I'm quite a private person. I'm much more comfortable in the studio."

Do's portrait is a favourite to win the People's Choice, which is voted for by visitors to the Archibald exhibition, and will be announced on September 11. His success in the Archibald Prize is no fluke – in the past 12 months, he has been a finalist in a number of art prizes and won the $8000 Kogarah Art Prize in July for Wombat Man.

Judge Anne Loxley, a curator at the Museum of Contemporary Art Australia, said Do's winning work was "a commanding portrait, and the bravura of his painting style is very impressive".

He was also a finalist in the Mosman Art Prize for his portrait of friend David Horton, a sculptor and teacher at the National Art School, and will have his first solo show at Olsen Irwin gallery in 2015.

Do uses Horton and fellow Archibald Prize finalist Paul Ryan to bounce ideas off and critique his work.

Says Horton: "What we've seen is he's just gotten better by the sheer fact he is making a lot of paintings and listening to criticism.

"He's got the means. He can afford good paints and good canvases. And there is an underlying talent there, anyway."

Do took up painting about four years ago, following the death of a close friend, enrolling in a TAFE course and enlisting Ryan's help to refine his work. Like his mentor, whose portrait of actor Richard Roxburgh is also in this year's Archibald Prize exhibition, Do lathers the canvas with thick layers of paint – a far cry from the days when he had money for neither.

"I'm drawn to the texture of it as well as the colour," Do says. "I love the accidental beautiful bits that can happen with thick paint when you just throw it on.

"What happens is it mixes itself. Because I have no idea what the paint is going to end up like, I often don't mix a colour completely."

It is a style reminiscent of many of Australia's top artists including Quilty and Nicholas Harding.

"I think he's coming through a particular style at the moment," Horton says. "Any good artist works through another artist's influence and then you gradually develop your own style."

The Archibald Prize is at the Art Gallery of NSW until September 28, before touring galleries in regional Victoria and NSW.

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