Feature selection is an important topic in data mining. In this paper, we focus on the problem in unsupervised scenario, which is challenging due to the absence of labels. We formulate our model RRCS from the viewpoint of selfrepresentation. For the selection matrix, unlike many previous methods which take the L2,1-norm regularization to avoid trivial solution and achieve feature selection, we directly use the L2,0-norm constraint to obtain a more accurate solution. By explicitly considering the representation residue, we relax the hard linear constraint in self-representation, making our model better deal with the nonlinear case. Using the L2,1- norm loss term, the robustness of RRCS is achieved. Moreover, we add a graph regularization to preserve the local structure of the original data. An efficient algorithm is derived to solve the regularized and constrained problem. Extensive experiments on several datasets demonstrate the effectiveness of the proposed method.