Violent dissident republicans are chief suspects for the attack.
Police arrived on the scene at Ardmonagh Parade in the Whiterock area after a report at 7.05 pm.
He has been taken to the Royal Victoria Hospital for treatment to his non-life threatening injuries.
Detective Inspector Pete Mullan of the Reactive and Organised Crime Branch said: “I would appeal to anyone with any information about this shooting to contact detectives at Musgrave Police Station on the non emergency number 101.
“Or if someone would prefer to provide information without giving their details, they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.”