The 37-year-old victim was walking in the Downfine Walk area of the Turf Lodge estate when he was approached by two men near the Holy Trinity Centre.
They dragged him through an alleyway before shooting him once in each calf and once in the thigh. His injuries are not believed to be life-threatening.
The attack happened at about 18:30 GMT on Friday.
Police have appealed for witnesses to contact them.
A 15-year-old boy was shot in the leg in the nearby Ballymurphy estate on Thursday morning.
SDLP Councillor Tim Attwood said:  "This is the second vicious gun attack in west Belfast in two days, following the shooting of a teenager in Ballymurphy on Thursday.
"The cowardly men, wearing hoods, engaged in these attacks have no place in our community.
"Everybody who believes in human rights and justice must condemn these attacks and give their unequivocal backing to the PSNI in their efforts to police our communities."

York Minster Police has been given the same powers as regular police officers within the minster's precinct.
Eight constables and the cathedral's head of security were sworn in at a special ceremony on Tuesday.
The force, established in the 13th Century, lost its powers in the 1930s when officers ceased to be attested.
York Minster is one of only a handful of cathedrals to maintain its own police force. Those that do have a police force include Liverpool's Anglican Cathedral, Canterbury Cathedral, St Peter's Basilica in Rome, and Washington's National Cathedral in Washington DC.
Mark Sutcliffe, Inspector of Cathedral Police at York Minster, said: "I feel very proud of the whole team for attaining their attestation.
"It has been an important day for everyone involved but also a significant milestone in the history of the force, which has played an important role in life at the cathedral for hundreds of years.
"The attestation and training the officers have completed ensures our cathedral constables have the professional skills and powers necessary to execute their duties."
Powers were returned to the force following the signing of a memorandum of understanding between the Chapter of York and the chief constable of North Yorkshire.
The memorandum recognises that although security provision inside the minster and its precinct remain the responsibility of cathedral constables, North Yorkshire Police will be responsible for investigating all crime.
Any arrested people will be handed over to North Yorkshire Police for transport and processing and the force will be responsible for the submission of prosecution files.
The Minster Police constabulary is thought to be the oldest continuing police service in the country.

Biggin Hill Airport wants to increase bank holiday and weekend opening times to increase the number of flights.
Director William Curtis said he feared the airport could be asked to help the UK meet increased demand for air travel if the extension was not granted.
Bromley Council has approved new hours "in principle".
The airport, which caters to the business and general aviation sectors, is pushing for an hours' extension on weekdays, five-and-a-half hours' extra flying time on Saturday, and a further four-hour increase on Sundays.
Mr Curtis was asked whether he was "scaremongering" about taking holiday airlines during a BBC London interview.
He said: "What we will do is to ensure that we have set our stall out in the business and general aviation sector and we won't therefore be potentially looked at later by government as a solution to the capacity crisis."
Councillor Stephen Carr, leader of Bromley Council, said the move had the needs of residents versus those of a successful airport "at the heart of" it.
Bromley Council said the length and timings of the extension were yet to be decided, and would be subject to noise controls and monitoring.
The agreement follows an eight-week consultation period which saw 76% of respondents support the plan, it said.
In total, the consultation received more than 41,000 responses, with 31,500 coming out in support of the proposals and about 10,000 against.
However, some have expressed concern at the council's decision.
Hugh Bance, of Bromley Residents Against Airport Development, said there were 200,000 people living under the flight path who would be affected.
A man has been shot three times in the legs in west Belfast.
[NEXT_CONCEPT]
A cathedral police force has been given back the power of arrest for the first time in nearly 80 years.
[NEXT_CONCEPT]
A small London airport needs to extend its hours to avoid being forced to take on holidaymakers and more commercial airlines, its boss has claimed.