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In this paper, we propose a highly accurate inpainting algorithm which reconstructs an image from a fraction of its pixels. Our algorithm is inspired by the recent progress of non-local image processing techniques following the idea of 'grouping and collaborative filtering'. In our framework, we first match and group similar patches in the input image, and then convert the problem of estimating missing values for the stack of matched patches to the problem of low-rank matrix completion, and finally obtain the result by synthesizing all the restored patches. In our algorithm, how to accurately perform patch matching process and solve the low-rank matrix completion problem are key points. For the first problem, we propose a robust patch matching approach, and for the second task, the alternating direction method of multipliers is employed. Experiments show that our algorithm has superior advantages over existing inpainting techniques. Besides, our algorithm can be easily extended to handle practical applications including rendering acceleration, photo restoration and object removal.