Abstract Inspired by the fact that the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used in various image processing studies. Nonetheless, nuclear norm based convex surrogate of the rank function usually over-shrinks the rank components since it treats different components equally, and thus may produce a result far from the optimum. To alleviate the aforementioned limitations of the nuclear norm, in this paper we propose a new method for image restoration via the non-convex weighted ℓp nuclear norm minimization (NCW-NNM), which is able to accurately impose the image structural sparsity and self-similarity simultaneously. To make the proposed model tractable and robust, the alternating direction method of multiplier (ADMM) framework is adopted to solve the associated non-convex minimization problem. Experimental results on various image restoration problems, including image deblurring, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed method outperforms many current state-of-the-art methods.