The family of two adults and two young children were forced to flee the address on Jeffcock Road in Wolverhampton after three men attacked their home at about 2am on Monday.
The men were seen on camera leaving a car on the road, before smashing a window at the front of the house and pouring fuel through into the front room, trying to ignite it and then fleeing the scene in the car, driven by a fourth man.
Luckily for the occupants, the attackers' attempt at setting the fuel alight did not take and they were able to escape unharmed.
Detectives from West Midlands Police have said they believe the attack to be a case of mistaken identity and have asked anyone with information to get in touch.
A spokesman for West Midlands Police said: "We need your help finding a gang of men who set fire to a family in home in what may have been a case of mistaken identity.
"Three men smashed a window at the property on Jeffcock Road, Wolverhampton, at around 2am yesterday (March 28) before pouring fuel inside.
"They lit it, but luckily it didn’t take hold and the adults and two young children inside managed to escape unharmed.
"The gang fled in a vehicle driven by a fourth person.
"Detectives believe the arson attack may have been a case of mistaken identity.
"Anyone with information has been asked to get in touch via Live Chat at west-midlands.police.uk, or via 101, quoting 20/334090/22.
"Alternatively, call Crimestoppers anonymously on 0800 555 111."