The covering multi-granularition rough sets obtained by maximum description and minimal description can be better applied to reality. Fristly, four kinds of pessimistic covering multi-granularition rough set models are defined by the minimal description and the maximum description, and then its basic proper is analyzed. Moreover, the belief struct of covering multi-granularition rough sets is analyzed. The sufficient conditions for the belief struct covering multi-granularition rough sets is obtained which is approximately satisfied the duality, additivity and multiplication. Through the above study, the research of multi-granularition rough sets is enriched.