feed off, feed off of, feed on

feed off (of) something: 

to eat something in particular customarily. (Of is usually retained before pronouns.) 

• This creature feeds off fallen fruit. 
• Mosquitoes seem to want to feed off of me!
  

feed (up)on someone or something:

to eat someone or something. (Upon is formal and less commonly used than on.) 

• They say that some Bengal tigers feed upon people. 
• They feed on anything that moves.
  

... http://idioms.thefreedictionary.com/feed