He was dragged into an alleyway in the Bread Street area at about 9pm on Thursday. The victim was taken to hospital for treatment to injuries which were not believed to be life-threatening.
Police are hunting two men who are suspected of involvement in the gun attack. They were dressed in black and fled in the direction of the Divis estate.
Police Service of Northern Ireland Detective Inspector Michelle Griffin has appealed for anyone with information to contact officers from the reactive and organised crime unit at Musgrave station on 101, quoting reference number 1320 29/09/16.
West Belfast MP Paul Maskey condemned the shooting as wrong.
He said: “There is no place for these type of actions in our society.
“Those responsible need to end their war against the community and stop these shootings immediately.”