It happened shortly before 20:00 GMT at Finn House flats in the New Lodge area.
He was taken to hospital but police said his injuries are "not believed to be life-threatening at this time".
Insp James Murphy appealed to anyone who saw suspicious activity in the New Lodge area to contact detectives on the non-emergency number 101.
A man has been shot in both legs in what police described as a paramilitary-style attack in north Belfast.