The brutal gun attack happened in a house in Norglen Parade, Turf Lodge, just after 6.15 pm this evening, Thursday, January 12.
Both the man and the woman, who were in their 50s, were shot in the legs and have been taken to the Royal Victoria Hospital for treatment.
Sinn Féin MLA Pat Sheehan said the victims had been “shot in their own living room”.
“Whatever the motivation, there is absolutely no justification for it.”
Mr Sheehan added that “a number of people” had been shot in the legs in separate attacks in Turf Lodge over the past six to nine months.
West Belfast MLA Alex Attwood, from the SDLP, described the gun attack as an “act of tyranny”.
“The fact that two people, a man and a woman and both in their 50s, have been injured confirms that no one is off limits to those who are now using the gun,” he said.
The PSNI remain at the scene and detectives from the force’s Reactive and Organised Crime Branch have appealed for witnesses.