Kim Kang-woo debuted in the movie The Coast Guard in 2002. The following year, he was cast in the MBC series Breathless, in which he was nominated for Best New Actor at the MBC Drama Awards. In 2004, he starred in the film Springtime, which earned him a Best New Actor nomination at the 3rd Korean Film Awards. In 2005, he took home the Best New Actor trophy at the 6th Busan Film Critics Awards for his work in the movie The Aggressives. In 2007, his performance in the film The Railroad won him Best Actor at the 25th Torino Film Festival. In 2009, 2012, and 2014, he scored nominations for an Excellence Award at the KBS Drama Awards for Story of a Man, Haeundae Lovers, and Golden Cross, respectively. In 2016, he became part of the main cast of the MBC manhwa-based drama Goodbye, Mr. Black. He was nominated for a Top Excellence Award at the MBC Drama Awards for the said series. In 2018, he headlined the MBC drama My Husband Oh Jak-doo, in which he picked up a Top Excellence Award at the MBC Drama Awards. In 2019, he received a nomination for an Excellence Award at the KBS Drama Awards for the thriller drama 9.9 Billion Won Woman.

Kim Kang-woo tied the knot with his long-time girlfriend Han Moo-young on June 18, 2010. Han Moo-young is the older sister of actress Han Hye-jin. The couple welcomed their son in 2011.