graze on

graze on something

 
1. [for animals] to browse or forage in a particular location. The cattle are grazing on the neighbor's land. I wish they wouldn't graze on other people's land.
2. [for animals] to browse or forage, eating something in particular. The deer are grazing on my carrots! The cows were grazing on the meadow grasses for weeks.
See also: graze, on