In recent years, the generation adversarial networks (GAN) family has been successfully applied for face age synthesis. Nevertheless, it is found that even if the conditional generation adversarial networks (CGAN) are good at using age prior information, the important age information will be discarded to some extent, when CGAN is used to address the problem of face age synthesis. This is an important factor that makes the performance of the GAN family represented by CGAN in face age synthesis task reach the bottleneck period. Therefore, a class-aware instance normalization (CAIN) is proposed, which can be flexibly embedded in CGANs, called CAIN-GAN, for thoroughly leveraging the age prior information to improve the performance of face age synthesis. Experiments on the public datasets show that the proposed CAIN-GAN can improve the performance of face age synthesis only by leveraging the face age-related information, compared with several GAN-based face age synthesis methods.