The family were at home in Whiterock Gardens when gunshots were fired through the window.
The attack took place at about 10pm on Wednesday and police are treating it as a hate crime.
The family, who are believed to be members of the Travelling community, were not injured.
A number of windows were broken at the house, where they are believed to have been living for less than a week.
Police have appealed for anyone with information to contact them on 101.
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