The incident happened at around 3pm on February 10 as the girl walked along the pathway at the back of Lancaster Priory.
She was heading towards Long Marsh Lane when she was approached by an unknown man walking in the opposite direction.
The man grabbed the girl by the arm and tried to pull her from the pathway she was walking on.
The girl managed to free herself and run away.
The man is described as being white with a pale complexion. He is said to be in his early 30s and around 6ft tall with skinny arms, hairy hands and big hips.
He was wearing glasses with a silver rim and small circular lenses, a black hoody with the hood up and a silver zip with either jogging bottoms or jeans.
DS Paul Richardson of Lancaster Police said: “The girl didn’t suffer any physical harm, however it has understandably left her scared and upset. We have a number of detectives working on this investigation.
“If you recognise the description or you have any information about this incident at all, please call us as soon as you can.”
Anyone with information should ring 101 quoting log number 937 of 10th February.
Alternatively independent charity Crimestoppers can be contacted anonymously on 0800 555111 online at http://socsi.in/zHLVb.