Achieving the generalization of an invariant classifier from source domains to shifted target domains while simultaneously considering model fairness is a substantial and complex challenge in machine learning. Existing domain generalization research typically attributes domain shifts to concept shift, which relates to alterations in class labels, and covariate shift, which pertains to variations in data styles. In this paper, by introducing another form of distribution shift, known as dependence shift, which involves variations in fair dependence patterns across domains, we propose a novel domain generalization approach that addresses domain shifts by considering both covariate and dependence shifts. We assert the existence of an underlying transformation model can transform data from one domain to another. By generating data in synthetic domains through the model, a fairness-aware invariant classifier is learned that enforces both model accuracy and fairness in unseen domains. Extensive empirical studies on four benchmark datasets demonstrate that our approach surpasses state-of-the-art methods.