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Lattice-based Identity-based encryption (IBE) can both simplify certificate management and resist quantum attack in the real world. Combined Public Key (CPK) technology can be used to enhance the efficiency of IBE schemes. In this paper, we use CPK to construct a more efficient lattice-based IBE scheme based on a variant of learning with errors (LWE) problem, by avoiding complex trapdoor generation algorithm and preimage sampling algorithm required by the existing lattice-based IBE schemes from LWE. Its storage cost is also lower. We show that our IBE scheme is semantically secure against an adaptive chosen plaintext attack (CPA) from all probabilistic polynomial time adversaries in the random oracle model.