In recent research, metric learning methods have attracted increasing interests in machine learning community and have been applied to many applications. However, the existing metric learning methods usually use a fixed L2-norm to measure the distance between pairwise data samples in the projection space, which cannot provide an effective mechanism to automatically remove the noise that exist in data samples. To address this issue, we propose a new robust formulation of metric learning. Our new model constructs a projection from higher dimensional Grassmann manifold into the one in a relative low-dimensional with more discriminative capability, where the errors between sample points are considered as an MLE (maximum likelihood estimation)-like estimator. An efficient iteratively reweighted algorithm is derived to solve the proposed metric learning model. More importantly, we establish the generalization bounds for the proposed algorithm by utilizing the techniques of U-statistics. Experiments on six benchmark datasets clearly show that the proposed method achieves consistent improvements in discrimination accuracy, in comparison to state-of-the-art methods.