Abstract: Based the factorial decompose theorem of polynomial with factors in a finite field, a new group signature schemes is proposed.The solution is efficient in that it needs no communication between group manager and member, and the member's key is not need to change when the group manager adds or excludes the group members.The signing is same as a normal signature, and the computational cost of verifying is independent of the number of the revoked members.At last, the security is analyzed under factorial decompose theorem of polynomial and discrete logarithm problem assumption.