The shooting happened at around 22:00 BST on Friday night in Ardmonagh Parade.
The victim was taken to hospital for treatment to his injuries which are not believed to be life-threatening.
SDLP justice spokesperson and west Belfast MLA Alex Attwood said: "There is a new tyranny emerging - drug pushing on one hand and violent attacks on the other."
"Many in west Belfast know the scale of the threat, the impact on our community and the risks for our young people in particular."
"People and police must together confront these criminal and violent forces," he added.
PSNI Det Insp Mark McHaffie has appealed for witnesses to contact police.
A 21-year-old man has been shot in both legs in the Turf Lodge area of west Belfast.