Grieve began his career in 1988 studying drama and dance at Victoria University in Melbourne. He then completed his formal training in Sydney, at the National Institute of Dramatic Art (NIDA). He joined the cast of "Neighbours" in 1994, playing the part of Sam Kratz until 1996 when he joined "Home and Away" playing Dr Lachlan Fraser. His other television credits include, "The Man From Snowy River, the series", "Newlyweds", "E Street", "State Coroner", and "Wintertime" for the Australian Broadcasting Corporation.