In Wasserstein GAN, it is important to regularize the discriminator to have a not big Lipschitz constant. In this paper, I introduce discriminator variance regularization to regularize the discriminator of Wasserstein GAN to have a small Lipschitz constant. Discriminator variance regularization simply regularizes the variance of the discriminator's output to be small when input is real data distribution or generated data distribution. Intuitively, a low variance of discriminator output implies that the discriminator is more likely to have a low Lipschitz constant. Discriminator variance regularization does not explicitly regularize the Lipschitz constant of discriminator through differentiation on discriminator but lowers the probability that the Lipschitz constant of the discriminator is high. Discriminator variance regularization is used in Wasserstein GAN with R1 regularization, which reduces the vibration of GAN. Discriminator variance regularization requires very little additional computing.