Despite the progress in voice conversion, many-to-many voice conversion trained on non-parallel data, as well as zero-shot voice conversion, remains under-explored. Deep style transfer algorithms, generative adversarial networks (GAN) in particular, are being applied as new solutions in this field. However, GAN training is very sophisticated and difficult, and there is no strong evidence that its generated speech is of good perceptual quality. In this paper, we propose a new style transfer scheme that involves only an autoencoder with a carefully designed bottleneck. We formally show that this scheme can achieve distribution-matching style transfer by training only on self-reconstruction loss. Based on this scheme, we proposed AutoVC, which achieves state-of-the-art results in many-to-many voice conversion with non-parallel data, and which is the first to perform zero-shot voice conversion.