Two devices were thrown at the property in Coleraine’s Mossvale Park shortly after midnight on Thursday.
The woman lives in the house with her children who are 13, 17 and 21.
They were not injured but, police said, they had been left “badly shaken”.
It is understood to be the third time the house has been targeted.
A window was smashed and scorch damage was caused to the front door.
It is believed to be the sixth petrol bomb attack in the town since April 24.
“These reckless attacks are not wanted by anyone and do nothing but cause harm and damage to the local community who we know just want to live in peace,” said Chief Inspector Sinead McIldowney.
She said attacks of this nature could result in devastating consequences and were completely unacceptable.
“I will again stress that people engaging in this type of criminal behaviour are risking not only their own safety, but they also face the possibility of a criminal conviction which can have life changing consequences,” she said.
The police have appealed for anyone with information to come forward and contact detectives on the 101 number.
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