We propose a new efficient group signature scheme based on Strong RSA assumption.Because the scheme doesn't adopt knowledge proof signature as building block

it is simple to sign algorithm and verify algorithm in the scheme

so that the primary merit of the scheme is that the total computation of signature and verification is only 9 exponent operations and much less than the state-of-the-art ACJT scheme in computation cost.Finally

we analyze the efficiency of the proposed scheme and show that the scheme is more efficient than group signature schemes such as ACJT scheme in complexity.