Abstract: Recently, much attention has been paid on Multi-granulation Rough Set (MGRS) and MGRS has been a promising topic in rough set theory. This study firstly proposes two kinds of covering multi-granulation rough set, namely, optimistic covering multi-granulation rough set and pessimistic covering multi-granulation rough set, on the basis of the maximal descriptors of elements in a given covering approximation space. And then, a number of basic properties of the two kinds of rough sets are discussed. Finally, the relationships among the models are disclosed.