The proxy re-encryption allows an intermediate proxy to convert a ciphertext for Alice into a ciphertext for Bob without seeing the original message and leaking out relevant information. Unlike many prior identity based proxy re-encryption schemes which are based on the number theoretic assumptions such as large integer factorization and discrete logarithm problem. In this paper, we first propose a novel identity based proxy re-encryption scheme which is based on the hardness of standard Learning With Error(LWE) problem and is CPA secure in the standard model. This scheme can be reduced to the worst-case lattice hard problem that is able to resist attacks from quantum algorithm. The key step in our construction is that the challenger how to answer the private query under a known trapdoor matrix. Our scheme enjoys properties of the non-interactivity, unidirectionality, anonymous and so on. In this paper, we utilize primitives include G-trapdoor for lattice and sample algorithms to realize simple and efficient re-encryption.