A subgroup H of G is called M-supplemented in G if there exists a subgroup B of G such that G =HB and HiB ＜ G for every maximal subgroup Hi of H.In this paper,we use M-supplemented subgroups to study the structure of finite groups and obtain some new characterization about solvability and p-supersolvability for a fixed prime p.Some results in the literature are corollaries of our theorems.