Generative Adversarial Networks (GANs) have demonstrated a strong ability to fit complex distributions since they were presented, especially in the field of generating natural images. Linear interpolation in the noise space produces a continuously changing in the image space, which is an impressive property of GANs. However, there is no special consideration on this property in the objective function of GANs or its derived models. This paper analyzes the perturbation on the input of the generator and its influence on the generated images. A smooth generator is then developed by investigating the tolerable input perturbation. We further integrate this smooth generator with a gradient penalized discriminator, and design smooth GAN that generates stable and high-quality images. Experiments on real-world image datasets demonstrate the necessity of studying smooth generator and the effectiveness of the proposed algorithm.