Bai (2010) and Bai et al. (2012) proposed robust mixture regression method based on the M regression estimation. However, the M-estimators are robust against the outliers in response variables, but they are not robust against the outliers in explanatory variables (leverage points). In this paper, we propose a robust mixture regression procedure to handle the outliers and the leverage points, simultaneously. Our proposed mixture regression method is based on the GM regression estimation. We give an Expectation Maximization (EM) type algorithm to compute estimates for the parameters of interest. We provide a simulation study and a real data example to assess the robustness performance of the proposed method against the outliers and the leverage points.