The homomorphic inner product has a wide range of applications such as secure multi-geometry calculation, private data mining, outsourced computing, and sortable ciphertext retrieval. However, the existing schemes for calculating the homomorphism inner product are mostly based on FHE by RLWE with low efficiency. With MLWE, this study proposes a homomorphic inner product scheme by using a low expansion rate encryption algorithm proposed by Ke, et al. Firstly, the tensor product operation in the cipher space is given, which corresponds to the integer vector product operation in the plaintext space. Then, the correctness and security of the scheme are analyzed. At last, two sets of optimized encryption parameters are given, corresponding to the different application scenarios of homomorphic inner product. The scheme of this study is implemented by C++ and the large integer computation library NTL. Compared with other homomorphic encryption schemes, this scheme can efficiently calculate the homomorphism inner products of integer vectors.