However, there are three types of zebras,  such as mountain, Grevy, and common … zebra species. These different  species may eat different types of grasses. For example, Grevy  zebras can eat coarse grasses and bark when grass is scarce. A  mountain zebra can eat tufted grass.Zebras also eat other foods  when grass sources are scarce, and these include roots, shrubs, and  even fruit.owever, there are three types of zebras,  such as mountain, Grevy, and common … zebra species. These different  species may eat different types of grasses. For example, Grevy  zebras can eat coarse grasses and bark when grass is scarce. A  mountain zebra can eat tufted grass.