This work presents an optimal design method of antenna aperture illumination for microwave power transmission with an annular collection area. The objective is to maximize the ratio of the power radiated on the annular collection area to the total transmitted power. By formulating the aperture amplitude distribution through a summation of a special set of series, the optimal design problem can be reduced to finding the maximum ratio of two real quadratic forms. Based on the theory of matrices, the solution to the formulated optimization problem is to determine the largest characteristic value and its associated characteristic vector. To meet security requirements, the peak radiation levels outside the receiving area are considered to be extra constraints. A hybrid grey wolf optimizer and Nelder-Mead simplex method is developed to deal with this constrained optimization problem. In order to demonstrate the effectiveness of the proposed method, numerical experiments on continuous apertures are conducted; then, discrete arrays of isotropic elements are employed to validate the correctness of the optimized results. Finally, patch arrays are adopted to further verify the validity of the proposed method.