Proxy re-encryption (PRE) securely enables the re-encryption of ciphertexts from one key to another, without relying on trusted parties, i.e., it offers delegation of decryption rights. PRE allows a semi-trusted third party termed as a "proxy" to securely divert encrypted files of user A (delegator) to user B (delegatee) without revealing any information about the underlying files to the proxy. To eliminate the necessity of having a costly certificate verification process, Green and Ateniese introduced an identity-based PRE (IB-PRE). The potential applicability of IB-PRE leads to intensive research from its first instantiation. Unfortunately, till today, there is no unidirectional IB-PRE secure in the standard model, which can withstand quantum attack. In this paper, we provide, for the first time, a concrete construction of unidirectional IB-PRE which is secure in standard model based on the hardness of learning with error problem. Our technique is to use the novel trapdoor delegation technique of Micciancio and Peikert. The way we use trapdoor delegation technique may prove useful for functionalities other than proxy re-encryption as well.