Petrol was poured through the letter box of a family home then ignited in an early hours arson attack.
The house in Quantock Gardens, Hastings, was targeted at about 5.45am on Sunday morning.
The family inside were awoken by a fire alarm and were able to extinguish the flames before they caused any major damage to the property.
Police investigating the incident say the ignition was deliberate and officers are now appealing for witnesses as they look to establish the circumstances surrounding the arson attack.
Detective Sergeant Robin Mitchell-Davis said; "We are treating this as a deliberate though isolated attack, which could have had the most serious consequences, and want to hear from anyone who saw what happened or who has any other information.
"If you can help please contact us either online or by calling 101, quoting serial 204 of 04/04.
"You can also contact the independent charity Crimestoppers anonymously on 0800 555 111."
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