A man and two women were in the house at Norglen Parade when a number of shots were fired through the front window at around 1.15 am.
Police have said they are trying to establish a motive for the attack and have appealed for information.
It is the second gun attack in west Belfast in the space of 48 hours.
Shots were fired at a house in nearby Tollnamona Court the early hours of Saturday.
At this stage the attacks are not being linked by detectives.