The endeavor to preserve the generalization of a fair and invariant classifier across domains, especially in the presence of distribution shifts, becomes a significant and intricate challenge in machine learning. In response to this challenge, numerous effective algorithms have been developed with a focus on addressing the problem of fairness-aware domain generalization. These algorithms are designed to navigate various types of distribution shifts, with a particular emphasis on covariate and dependence shifts. In this context, covariate shift pertains to changes in the marginal distribution of input features, while dependence shift involves alterations in the joint distribution of the label variable and sensitive attributes. In this paper, we introduce a simple but effective approach that aims to learn a fair and invariant classifier by simultaneously addressing both covariate and dependence shifts across domains. We assert the existence of an underlying transformation model can transform data from one domain to another, while preserving the semantics related to non-sensitive attributes and classes. By augmenting various synthetic data domains through the model, we learn a fair and invariant classifier in source domains. This classifier can then be generalized to unknown target domains, maintaining both model prediction and fairness concerns. Extensive empirical studies on four benchmark datasets demonstrate that our approach surpasses state-of-the-art methods.