The attack happened in Teeling Avenue in Dunmurry early this morning, Sunday 28 October.
At around 5.30am police received a report that a black bin had been placed at the rear door of the property and set alight.
Thankfully the female owner of the property was able to extinguish the fire.
The property sustained smoke damage as a result.
Detectives are treating the incident as arson with intent to endanger life.
Detective Sergeant McCallum is appealing for anyone who witnessed the incident or anyone with any information that can assist with the investigation to contact detectives in Musgrave on 101 quoting reference 427 28/10/18.
Alternatively, information can also be provided to the independent charity Crimestoppers on 0800 555 111, which is 100% anonymous and gives people the power to speak up and stop crime