We don't see the Predator (Yautja) eating anything in the films. All evidence from the EU points toward them being omnivourous but with an emphasis on eating *raw* meat and veg.

> **[Predator: Strange Roux][1]** - *Muskrat meat.*

> [![enter image description here][2]][2]

and

> **[Predator: Homeworld][3]** - *Some sort of root.*

> [![enter image description here][4]][4]

They also drink an (alcoholic?) intoxicating beverage called c'ntlip

> Unbidden came a memory. Of a time when he and his brother had sat
> drinking c'ntlip, the fiery brew that fogged mind and body with
> pleasure. Someday they would be Leaders, not only of ships but of
> other Leaders. Great would be their fame. Stories would be sung of
> their Hunts for a thousand years, each of them was certain.

> <sub><sup>[AVP: Prey][5]</sub></sup>


  [1]: http://avp.wikia.com/wiki/Predator:_Strange_Roux
  [2]: https://i.sstatic.net/iLV7x.png
  [3]: http://avp.wikia.com/wiki/Predator:_Homeworld
  [4]: https://i.sstatic.net/0wfJH.png
  [5]: http://avp.wikia.com/wiki/Aliens_vs._Predator:_Prey