Recently, sparse unmixing (SU) of hyperspectral data has received particular attention for analyzing remote sensing images. However, most of SU methods are based on the commonly admitted linear mixing model (LMM), which ignores the possible nonlinear effects (i.e. nonlinearity). In this paper, we proposed a new method named robust collaborative sparse regression (RCSR) for hyperspectral unmixing, which is based on the robust LMM (rLMM). The rLMM takes the nonlinearity into consideration, and the nonlinearity is merely treated as outlier, which has the underlying sparse property. The RCSR takes the collaborative sparse property of the abundance and sparsely distributed additive property of the outlier into consideration, which can be formed as a robust joint sparse regression problem. Experiments on synthetic datasets demonstrate that the proposed RCSR is efficient for solving the hyperspectral SU problem compared with other five state-of-the-art algorithms.