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Generative adversarial networks (GANs) are powerful generative models, but usually suffer from instability and generalization problem which may lead to poor generations. Most existing works focus on stabilizing the training of the discriminator while ignoring the generalization properties. In this work, we aim to improve the generalization capability of GANs by promoting the local robustness within the small neighborhood of the training samples. We also prove that the robustness in small neighborhood of training sets can lead to better generalization. Particularly, we design a robust optimization framework where the generator and discriminator compete with each other in a \textit{worst-case} setting within a small Wasserstein ball. The generator tries to map \textit{the worst input distribution} (rather than a Gaussian distribution used in most GANs) to the real data distribution, while the discriminator attempts to distinguish the real and fake distribution \textit{with the worst perturbation}. We have proved that our robust method can obtain a tighter generalization upper bound than traditional GANs under mild assumptions, ensuring a theoretical superiority of RGAN over GANs. A series of experiments on CIFAR-10, STL-10 and CelebA datasets indicate that our proposed robust framework can improve on five baseline GAN models substantially and consistently.