The victim has been named locally as Joe Reilly.
The attack was carried out by dissident republican gunmen.
The victim, who was aged 48, was shot dead at a house in Glenwood Court in the Poleglass area.
The shooting was reported to police at about 8.15 pm on Thursday night.
It is understood the man was tended to by paramedics at the scene who described his injuries as serious.
However, the victim later died in the RVH from his injuires.
Local Sinn Fein MLA Jennifer McCann said it “appeared someone went into a house here in Glenwood and shot a man”.
She added: “The family have been coming up here, there’s been quite distraught scenes with the family trying to get in to see him.”
West Belfast SDLP MLA Alex Attwood said: “I completely condemn the latest barbaric attack on a man in west Belfast.
“These savage assaults had no place in our past and they have no place in our society today.”
Dissident republican terror group Oglaigh na hEireann (ONH) have carried out two recent shootings.
Peter Lagan, 56, was shot six times last Sunday in nearby Glenwood Drive.
Shadowy ONH has warned in a doorstep notice to residents that it tried to kill a man recently.
It is not yet known if last night’s victim was the same man they tried but failed to murder who they had ordered to leave the country on pain of death.