Recently, deep generative models have become increasingly popular in unsupervised anomaly detection. However, deep generative models aim at recovering the data distribution rather than detecting anomalies. Moreover, deep generative models have the risk of overfitting training samples, which has disastrous effects on anomaly detection performance. To solve the above two problems, we propose a self-adversarial variational autoencoder (adVAE) with a Gaussian anomaly prior assumption. We assume that both the anomalous and the normal prior distribution are Gaussian and have overlaps in the latent space. Therefore, a Gaussian transformer net T is trained to synthesize anomalous but near-normal latent variables. Keeping the original training objective of a variational autoencoder, a generator G tries to distinguish between the normal latent variables encoded by E and the anomalous latent variables synthesized by T, and the encoder E is trained to discriminate whether the output of G is real. These new objectives we added not only give both G and E the ability to discriminate, but also become an additional regularization mechanism to prevent overfitting. Compared with other competitive methods, the proposed model achieves significant improvements in extensive experiments. The employed datasets and our model are available in a Github repository.