When data is outsourced to a remote storage server, searchable encryption plays an important role to protect data privacy while allowing users to retrieve data in the massive ciphertext. As far as we know, most of the existing searchable encryption schemes work based on the bilinear map. These schemes may not be secure in the quantum age. Both discrete logarithms and factorization can be solved by quantum computer in a polynomial time. There are very few searchable encryption schemes that can be proved secure in post quantum age. In this paper, in order to construct a post-quantum secure scheme for future cloud storage, we suggest a public key encryption with semantic keyword search using the lattice based mechanism. The suggested scheme is proved secure against indistinguishable chosen-keyword attacks (IND-CKA) based on learning with errors (LWE) problem. This scheme is believed to be secure in quantum-era due to the quantum intractability of the LWE problem.