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In medical imaging and astronomical observation, high-resolution (HR) images are urgently desired and required. In recent years, many researchers have proposed various ways to achieve the goal of image super-resolution (SR), ranging from simple linear interpolation schemes to nonlinear complex methods. In this paper, we deal with the SR reconstruction problem based on the theory of compressive sensing, which uses a redundant dictionary instead of a conventional orthogonal basis. We further demonstrate better results on true images in terms of peak signal-to-noise ratio (PSNR) and root-mean-square error (RMSE) and give several important improvements, compared with other methods.