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Although significant progress has been made in face recognition, demographic bias still exists in face recognition systems. For instance, it usually happens that the face recognition performance for a certain demographic group is lower than the others. In this paper, we propose MixFairFace framework to improve the fairness in face recognition models. First of all, we argue that the commonly used attribute-based fairness metric is not appropriate for face recognition. A face recognition system can only be considered fair while every person has a close performance. Hence, we propose a new evaluation protocol to fairly evaluate the fairness performance of different approaches. Different from previous approaches that require sensitive attribute labels such as race and gender for reducing the demographic bias, we aim at addressing the identity bias in face representation, i.e., the performance inconsistency between different identities, without the need for sensitive attribute labels. To this end, we propose MixFair Adapter to determine and reduce the identity bias of training samples. Our extensive experiments demonstrate that our MixFairFace approach achieves state-of-the-art fairness performance on all benchmark datasets.