In this paper, we develop a face recognition system with the derived subspace learning method, i.e. classifier-concerning subspace, where not only the discriminant structure of data can be preserved but also the classification ability can be explicitly considered by introducing the Mahalanobis distance metric in the subspace. Most of graph-based subspace learning methods find a subspace with the preservation of certain geometric and discriminant structure of data but not explicitly include the classification information from the classifier. Via the distance metric, which is constrained by k-NN classification rule, the pairwise distance relation can be locally adjusted and thus the projected data in the classifier-concerning subspace are more suitable for k-NN classifier. In addition, an iterative procedure is derived to get rid of the overfitting problem. Experimental results show that the proposed system can yield the promising recognition results under various lighting, pose and expression conditions.