Variational autoencoders (VAEs) have shown a promise in data-driven conversation modeling. However, most VAE conversation models match the approximate posterior distribution over the latent variables to a simple prior such as standard normal distribution, thereby restricting the generated responses to a relatively simple (e.g., single-modal) scope. In this paper, we propose DialogWAE, a conditional Wasserstein autoencoder (WAE) specially designed for dialogue modeling. Unlike VAEs that impose a simple distribution over the latent variables, DialogWAE models the distribution of data by training a GAN within the latent variable space. Specifically, our model samples from the prior and posterior distributions over the latent variables by transforming context-dependent random noise using neural networks and minimizes the Wasserstein distance between the two distributions. We further develop a Gaussian mixture prior network to enrich the latent space. Experiments on two popular datasets show that DialogWAE outperforms the state-of-the-art approaches in generating more coherent, informative and diverse responses.