Abstract: Proxy re-signature is an important tool for simplifying key management, and can be used to prove a proof for a path, manage group signatures, simplify certificate management and so on. Currently, proxy re- signature schemes are based on large integer factorization and discrete logarithm which are not security in quantum setting. For this problem, the first identity-based proxy re-signature scheme over lattices is constructed in this paper, which uses preimage sampleable technology and lattice basis delegation in fixed dimension technology. Its security is based on the hardness of Small Integer Solution (SIS) problem. This scheme possesses the properties of unidirectional, multi-use and so on. Compared with the previous schemes which have the same properties, the proposed scheme has the advantage of low verification cost and low asymptotic computational complexity.