Abstract: A subgroup H is called c₁-supplemented in Gif there is a subgroup K such that G=HK and H∩T≤Z_∞(G)，where Z_∞(G) is the hypercenter of G. It investigates the influence of the c₁-supplementation of subgroups on the structure of finite groups. The following results which generalize some related known results are obtained. Main Theorem: For any prime divisor p of |G|, let P be a Sylow p-subgroup of a group G. Suppose that P has a subgroup D satisfying the condition that 1<|D|<|P| and each subgroup of P of order |D|and p|D|is c₁-supplemented in G. Then G is supersolvable.

Key words: finite groups；c₁-supplemented subgroups；supersolvable groups