A reward for capturing or killing someone, usually someone guilty of a crime. For example, He was a serial killer, and they put a price on his head. The head in this term presumably alludes to the older punishment of beheading. [Mid-1700s]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.