Most traditional face recognition systems attempt to achieve a low recognition error rate, implicitly assuming that the losses of all misclassifications are the same. In this paper, we argue that this is far from a reasonable setting because, in almost all application scenarios of face recognition, different kinds of mistakes will lead to different losses. For example, it would be troublesome if a door locker based on a face recognition system misclassified a family member as a stranger such that she/he was not allowed to enter the house, but it would be a much more serious disaster if a stranger was misclassified as a family member and allowed to enter the house. We propose a framework which formulates the face recognition problem as a multiclass cost-sensitive learning task, and develop two theoretically sound methods for this task. Experimental results demonstrate the effectiveness and efficiency of the proposed methods.