In Pawlak rough set model, an element is in a set, or not in the set, or possibly in the set. A subset of objects, possibly in the set is called boundary of the set. In the research on Pawlak rough set model, less is paid to the research of the boundary issue. In this paper, two objects with a few minor differences in the degree of membership in a set are viewed in the same level. From this view a partition of the boundary of a rough set is obtained and the concepts of band rough set and band distribution reduction and maximum distribution reduction are presented. The judgment theorems, discernibility matrices, equivalence condition of core attribute association with band distribution reduction and band maximum distribution reduction are given .Band rough set model is a generalization of the Pawlak rough set and of the variable precision rough set model.