Curtis was born in Rotorua in 1968.[3] He is one of eight children born to George Curtis, an amateur dancer.[4] He is of Māori descent; his tribal affiliations are Te Arawa[5] and Ngāti Hauiti. His uncle was Toby Curtis, a prominent Māori educator and leader.
His first feature film role was a small part in the Oscar-nominated Jane Campion film The Piano. He went on to win attention in Once Were Warriors, one of the most successful films released on New Zealand screens; the line "Uncle fucken Bully" referring to Curtis's character spoken by "Jake the Muss", played by Temuera Morrison, became one of New Zealand film's most memorable and quoted lines, as well as being part of the "Kiwiana" trend. He played Kahu in the short-film Kahu & Maia, a contemporary depiction of a Ngāti Kahungunu and Ngāti Rongomaiwahine legend. He played a seducer in the melodrama Desperate Remedies. In 2000 Curtis starred as family man Billy Williams in Jubilee,[9] before playing father to the lead character in the international hit Whale Rider.
In 2004 with producer Ainsley Gardiner, Curtis formed independent film production company Whenua Films.[10] The goals of the company are to support the growth of the New Zealand indigenous film-making scene, and support local short filmmakers. He and Gardiner were appointed to manage the development and production of films for the Short Films Fund for 2005–06 by the New Zealand Film Commission. They have produced several shorts under the new company banner, notably Two Cars, One Night, which received an Academy Award nomination in 2005, and Hawaikii by director Mike Jonathan in 2006. Both short films circulated through many of the prestigious international film festivals like the Berlinale.
At the 2006 Cannes Film Festival, Miramax Films bought US distribution rights to relationship comedy Eagle vs Shark, the first feature film directed by Taika Waititi. Waititi's follow-up feature Boy, also from Whenua Films, went on to become the highest grossing New Zealand film released.[11]
In 2014, Curtis played the lead role in The Dark Horse, which the National Radio review called "one of the greatest New Zealand films ever made."[12] The New Zealand Herald praised him for his "towering performance"[13] as real-life Gisborne speed chess player and coach Genesis Potini, who died in 2011. Curtis studied chess and deliberately put on weight for the role.
He was married in late 2009[22] in a private ceremony at his home, and has four children. He is Roman Catholic.[23]
When asked about being an "all-purpose ethnic" actor, he said, "It's been a real advantage, I love being ethnic, I love the color of my skin. There are limitations in the business, that's a reality, but I've been given such wonderful opportunities."[24]