According to the characteristics of the staring imaging of Jilin-1 No.3 video satellite, in order to improve the spatial resolution of the image and overcome the insufficient resolution of optical system, a new algorithm of super-resolution reconstruction of a video satellite,intermediate convex sets mapping, is proposed. The characteristics of satellite staring imaging are analyzed based on the active view, and the degraded model is established based on the staring imaging. In order to solve the inverse process of the degraded model, the residual constraint set and the corresponding point projection operators in the intermediate degradation process are set up based on the convex set theory. The gray value of the high resolution image is corrected by the point projection operators, and finally the reconstructed high resolution image is constrained to the intersection of convex sets. The experimental results show that the new algorithm improves the image resolution by nearly 30%, and overcomes the disadvantages of the similar algorithms such as projection error and overlapping artifact. The image quality evaluation index is better than that of the other algorithms, and the convergence solution of the eight frames is obtained. It is feasible and robust to the image reconstruction with different definitions. All those show that the new algorithm is suitable for the super-resolution reconstruction of video satellite images.