Curry gained early drama experience at Track Youth Theatre.
In 2001, Curry had a lead role in the short-lived sitcom Sit Down, Shut Up. Also in 2001, he had a role in the mini-series Changi.
Between 2004 and 2005, Curry had a regular role in drama series The Secret Life of Us. He also appeared towards the end of the third series of Frontline taking over from Torquil Neilson as the sound recorder.
Curry has been a guest on Rove Live on several occasions. He has also appeared on the TV comedy series Thank God You're Here and Spicks and Specks several times, and has once been a guest on Talkin' 'bout Your Generation.
Since 2005, he has appeared in several Toyota Memorable Moments advertisements featuring iconic Australian rules football players of yesteryear Wayne Harmes, James Hird, Peter Daicos, Dermott Brereton, Malcolm Blight, Alex Jesaulenko, Tony Lockett, Francis Bourke, Bruce Doull and Kevin Bartlett and most recently Leigh Matthews with fellow comedian Dave Lawson, doing deliberately over-the-top reenactments of well-known moments of historic matches.
In 2007, Curry portrayed Graham Kennedy in The King, a telemovie examining Kennedy's life. The role required Curry to lose 14 kilograms. Also in 2007, Stephen appeared in The Librarians on a recurring basis as a tour guide.
In 2008, Curry hosted the 50th AFI Awards for the Nine Network.
In 2009, Curry had a role in the mini-series False Witness, a role in 30 Seconds and a guest role in Wilfred.
In 2011, Curry played Sam Pickles in the Australian drama Cloudstreet, which is based on the novel of the same name by Tim Winton.
In 2012, Curry guest starred in an episode of the Australian lawyer-drama Rake as Alex Alford. His character was accused of cutting off the "membrum virīle" (penis) of his neighbour.
From 2012 to 2013, He was part of the rotating cast of the Acclaimed Australian Drama series Redfern Now as policeman Ryan Hobbs.
During 2013 and 2014, Curry starred in the ABC drama series The Time Of Our Lives.
Curry started out in small roles in film, including The Castle and The Wog Boy. He then went to have leading roles in film, such as The Nugget, Take Away and Thunderstruck. In 2007, he was in the Australian film Rogue and also appeared in one of the finalist films, Pig Latin for the 2007 Sony Tropfest.
In 2011, he made The Cup, a biopic where he plays jockey Damien Oliver in the 2002 Melbourne Cup.
In 2012, he appeared as a reporter, in Cliffy, an Australian film based on the efforts of a marathon running 61-year-old potato farmer from Victoria, Cliff Young.
Curry starred in the 2012 film Save Your Legs! (Released 2013) as Abbotsford Anglers Cricket Club President Edward "Teddy" Brown.
Throughout 2010, Curry toured with Shaun Micallef on their Peter Cook/Dudley Moore tribute Good Evening, a show that was very well received by critics and public alike.
Curry won the 'Best Lead Actor in a Television Drama' award at the 2007 AFI Award's and the 'Most Outstanding Actor' award at the 2008 Logies for his role in The King.
Curry was born in Melbourne in 1976. He has two brothers who are also television and film actors – Andrew Curry and Bernard Curry.
Curry and wife Naadein Crowe married in a small ceremony in Bali on October 2010. After the wedding Curry and his wife Naadein performed a cultural ceremony in cooking Anjing Bakar with water spinach and jackfruit curry..
Curry is an Ambassador for Save the Children Australia.