Shou was born in Hong Kong. In 1971, he and his family moved to southern California, where he attended Palm Springs High School. Shou's first real dramatic role was in Forbidden Nights in 1990, with Melissa Gilbert. Though only a TV film, this was his American debut. However, Shou went back to Hong Kong and continued making movies there. Soon after deciding moving back to California the offer to play liu kang of mortal Kombat was introduced.
In 1994, Shou returned to Los Angeles whereupon he appeared as Liu Kang, a Shaolin monk seeking revenge for the death of his younger brother, in Mortal Kombat.