The wave back restoration of space object images is usually performed by restoration methods for nature optical images, however, the restoration effect is not ideal. This article proposes a restoration model of a space object image based on non-convex sparsity regularization according to the approximate sparsity of the space object image and the features that the gray value submits to Hyper-Laplace distribution in a regularization way. With the alternating direction multiplier method, the restoration model is split into two sub-problems in the numerical solving process: Fast Fourier transformation is used to solve the convex sub-problem, while the fixed-point iteration is used to solve the nonconvex sub-problem. Then, it gives a complete process for the proposed wave back restoration method of space object images, and do an experiment to test and verify the simulated images and the real space object images. Compared results show that proposed method improves the largest peak signal to noise ratio by 2 dB, the average structural similarity by 0.17 and the information entropy and the image definition by 3.85 and 2.65, respectively.