Face recognition is known to exhibit bias - subjects in certain demographic group can be better recognized than other groups. This work aims to learn a fair face representation, where faces of every group could be equally well-represented. Our proposed group adaptive classifier, GAC, learns to mitigate bias by using adaptive convolution kernels and attention mechanisms on faces based on their demographic attributes. The adaptive module comprises kernel masks and channel-wise attention maps for each demographic group so as to activate different facial regions for identification, leading to more discriminative features pertinent to their demographics. We also introduce an automated adaptation strategy which determines whether to apply adaptation to a certain layer by iteratively computing the dissimilarity among demographic-adaptive parameters, thereby increasing the efficiency of the adaptation learning. Experiments on benchmark face datasets (RFW, LFW, IJB-A, and IJB-C) show that our framework is able to mitigate face recognition bias on various demographic groups as well as maintain the competitive performance.