Abstract: In this paper, we establish an image denoising model and propose a new image denoising algorithm based on the study of sparse representation and dictionary learning theory. Homotopy method is used to learn a dictionary, which has the characteristics of fast convergence speed and high accuracy in signal recovery. As we can use the OMP algorithm to derive the sparse representation of the noisy image with respect to the learned dictionary, which is learned by the homotopy method, then by combining the sparse denoising model we can use our proposed method to denoise the noisy image. Experiment results show that the proposed algorithm can achieve nice performance for different noise environments. In the experiment of comparing the convergence speed with K-SVD algorithm, the experiment results sufficiently show that the proposed method has faster implementation than K-SVD which fully displays the advantage of using the homotopy method in learning a dictionary.