Firstly, the diffraction field distribution of a two-dimensional sinusoidal grating is derived through theoretical deduction, and based on the Fraunhofer diffraction theory, the expression of the field distribution in the target plane for a Laguerre-Gaussian beam passing through the grating is obtained. The numerical simulation results show that when a Laguerre-Gaussian beam passes through a two-dimensional phase sinusoidal grating generated by orthogonal overlapping of two one-dimensional gratings with same frequency and period, an N*N array of vortex beams consisting of the same topological charge is generated at the target plane. However, the intensities of vortex beams with different diffraction orders are unequal. To overcome this drawback, the grating is optimized using the Simulated Annealing algorithm. A 3*3 array with optical intensity inhomogeneity of 0.11‱ and diffraction efficiency of 81%, a 4*4 array with optical intensity inhomogeneity of 0.03‱ and diffraction efficiency of 72%, and a 5*5 array with optical intensity inhomogeneity of 5% and diffraction efficiency of 71% are obtained. The results demonstrate the simplicity and practicality of this method for generating vortex beam array, which will provide technical support for the application of vortex beam array with the same topological charge.