Recently, regression analysis based classification methods are popular for robust face recognition. These methods use a pixel-based error model, which assumes that errors of pixels are independent. This assumption does not hold in the case of contiguous occlusion, where the errors are spatially correlated. Furthermore, these methods ignore the whole structure of the error image. Nuclear norm as a matrix norm can describe the structural information well. Based on this point, we propose a nuclear-norm regularized regression model and use the alternating direction method of multipliers (ADMM) to solve it. We thus introduce a novel robust nuclear norm regularized regression (RNR) method for face recognition with occlusion. Compared with the existing structured sparse error coding models, which perform error detection and error support separately, our method integrates error detection and error support into one regression model. Experiments on benchmark face databases demonstrate the effectiveness and robustness of our method, which outperforms state-of-the-art methods.