Achieving fairness in learning models is currently an imperative task in machine learning. Meanwhile, recent research showed that fairness should be studied from the causal perspective, and proposed a number of fairness criteria based on Pearl's causal modeling framework. In this paper, we investigate the problem of building causal fairness-aware generative adversarial networks (CFGAN), which can learn a close distribution from a given dataset, while also ensuring various causal fairness criteria based on a given causal graph. CFGAN adopts two generators, whose structures are purposefully designed to reflect the structures of causal graph and interventional graph. Therefore, the two generators can respectively simulate the underlying causal model that generates the real data, as well as the causal model after the intervention. On the other hand, two discriminators are used for producing a close-to-real distribution, as well as for achieving various fairness criteria based on causal quantities simulated by generators. Experiments on a real-world dataset show that CFGAN can generate high quality fair data.