The attribute based signature scheme could verify the signature by the attribute instead of public key. But, a large number of bilinear operations are concentrated in the verification process, so the amount of computation required for signature verification is much larger than that of signature generation. To solve this problem, this paper proposed an attribute based signature scheme with aided-verification, which outsources the bilinear mapping. It supports LSSS matrix, with flexible expression ability. It proved the unforgeability and outsourcing computational completeness under chosen plaintext attack with the Diffie-Hellman problem assumption. The proposal could be used in mobile devices with limited computing power.