Paterson, et al. have studied identity-based signature scheme based on Waters’ signature scheme in a standard model, which has proved to have a security reduction to CDHP assumption, but has low computational efficiency. Although Li-Jiang, et al. improves Paterson’s scheme, Li-Jiang’s scheme has low online computational efficiency. This paper shows a more efficient identity-based signature scheme based on Paterson’s scheme in standard model. The new scheme improves computational efficiency by changing multiplicative operation to addition operation and pre-computing bilinear pairing operation. The scheme comparing with Paterson’s scheme decreases the number of multiplicative operation and the number of bilinear pairing operation of verifier. The scheme comparing with Li-Jiang’s scheme decreases the on-line computation of signer and verifier and the output parameters of system. Also, the scheme has proved to have a security reduction to CDHP assumption and the existential unforgeability under an adaptive chosen message attack. Comparing with other identity-based signature schemes in standard model, the new scheme is more efficient.