Achieving the generalization of an invariant classifier from training domains to shifted test domains while simultaneously considering model fairness is a substantial and complex challenge in machine learning. Existing methods address the problem of fairness-aware domain generalization, focusing on either covariate shift or correlation shift, but rarely consider both at the same time. In this paper, we introduce a novel approach that focuses on learning a fairness-aware domain-invariant predictor within a framework addressing both covariate and correlation shifts simultaneously, ensuring its generalization to unknown test domains inaccessible during training. In our approach, data are first disentangled into content and style factors in latent spaces. Furthermore, fairness-aware domain-invariant content representations can be learned by mitigating sensitive information and retaining as much other information as possible. Extensive empirical studies on benchmark datasets demonstrate that our approach surpasses state-of-the-art methods with respect to model accuracy as well as both group and individual fairness.