Mixed noise removal has been a challenging task due to the complex noise distribution. One representative type of mixed noise is the additive white Gaussian noise (AWGN) coupled with impulse noise (IN). Most mixed noise removal methods first detect and restore impulse pixels using median-type filters, and then perform AWGN removal. Such mixed noise removal methods, however, are less effective in preserving image structures, and tend to over-smooth image details. In this paper, we present a novel mixed noise removal method by proposing a weighted low rank model (WLRM). By grouping image nonlocal similar patches as a matrix, we reconstruct the clean image by finding the weighted low rank approximation or representation of the matrix. IN can be well suppressed by the adaptive weight setting, while the image global structure and local edges can be well preserved via the low rank model fitting. The weight setting and low rank model fitting are jointly optimized in WLRM. Our experiments validate that WLRM leads to very promising mixed noise removal results in terms of both quantitative measure and visual perception.