Optical computing is a new method to implement signal processing functions. The multiplication between a vector and a matrix is an important arithmetic algorithm in the signal processing domain. The optical vector-matrix multiplier (OVMM) is an optoelectronic system to carry out this operation, which consists of an electronic module and an optical module. In this paper, we propose an optical module for OVMM. To eliminate the cross talk and make full use of the optical elements, an elaborately designed structure that involves spherical lenses and cylindrical lenses is utilized in this optical system. The optical design software package ZEMAX is used to optimize the parameters and simulate the whole system. Finally, experimental data is obtained through experiments to evaluate the overall performance of the system. The results of both simulation and experiment indicate that the system constructed can implement the multiplication between a matrix with dimensions of 16 by 16 and a vector with a dimension of 16 successfully.