Conventional locality preserving projection aims to minimize recognition error rate, implicitly assuming the losses of different misclassifications are the same. However, this may not hold in many real world face recognition applications. Face recognition is a multiclass cost sensitive and class imbalance task. For example, it will be troublesome if a gallery person is misclassified as an impostor, but it will be much more costly if an impostor is misclassified as a gallery person. Consequently, different kinds of mistakes will lead to different losses. Moreover, the examples of gallery person from any class are fewer than examples of the impostor, which is referred to as class imbalance. For that, this paper integrates the misclassification costs into an objective function of the locality preserving projection and proposes a cost sensitive locality preserving projection that minimizes the misclassification costs. Simultaneously, a weight strategy is used to balance the contribution of each class to the projection. Experimental results on AR, PIE, Extended Yale B datasets demonstrate the superiority of the proposed method.