a price on (one's) head
An amount of money being offered as a reward for one's capture, or, in some cases, killing. I'm sorry, but we can't travel with your brother any longer. The sheriff has put a price on his head and it's too dangerous for the rest of us! I'll never be able to live peacefully in this town as long as I have a price on my head.
a price on someone's head
If there is a price on someone's head, someone has offered money if they are caught or killed. He had twice fled the area with a price on his head.
a price on someone's head
a reward offered for someone's capture or death.