Police said accelerant was poured through the letter box of a house at St Agnes Place and set alight at about 22:30 BST on Wednesday.
The fire was put out before emergency services arrived. It damaged the front door and caused some smoke damage to the house.
The children, and two women aged 23 and 61, were unharmed.
Police said they are working to establish a motive for the attack and want to hear from witnesses. Detectives can be contacted at Musgrave Police Station by calling 101.
Three children aged between four and six and two women have escaped injury in an arson attack in west Belfast.