Non-parallel many-to-many voice conversion is recently attract-ing huge research efforts in the speech processing community. A voice conversion system transforms an utterance of a source speaker to another utterance of a target speaker by keeping the content in the original utterance and replacing by the vocal features from the target speaker. Existing solutions, e.g., StarGAN-VC2, present promising results, only when speech corpus of the engaged speakers is available during model training. AUTOVCis able to perform voice conversion on unseen speakers, but it needs an external pretrained speaker verification model. In this paper, we present our new GAN-based zero-shot voice conversion solution, called GAZEV, which targets to support unseen speakers on both source and target utterances. Our key technical contribution is the adoption of speaker embedding loss on top of the GAN framework, as well as adaptive instance normalization strategy, in order to address the limitations of speaker identity transfer in existing solutions. Our empirical evaluations demonstrate significant performance improvement on output speech quality and comparable speaker similarity to AUTOVC.