Inspired by Agrawal, Boneh and Boyen's identity-based encryption scheme, we proposed a post-quantum identity-based signature scheme from lattices. In this construction, two distinct trapdoors are used to find short bases. One trapdoor enables the real implementation to generate short bases for all lattices. The other trapdoor enables the simulator to generate short bases for all lattices. Moreover, the generating short bases are used to sample short vectors as signatures. Based on the hardness of the small integer solution (SIS) problem, the proposed scheme is proven to be strongly unforgeable against adaptive chosen-identity and adaptive chosen-message attacks without using random oracles. Compared with the existing strongly unforgeable identity-based signature schemes, our scheme has the advantages of full security and resistance to quantum computing attacks.