Zero-shot cross-domain dialogue state tracking (DST) enables us to handle task-oriented dialogue in unseen domains without the expense of collecting in-domain data. In this paper, we propose a slot description enhanced generative approach for zero-shot cross-domain DST. Specifically, our model first encodes dialogue context and slots with a pre-trained self-attentive encoder, and generates slot value in an auto-regressive manner. In addition, we incorporate Slot Type Informed Descriptions that capture the shared information across different slots to facilitate cross-domain knowledge transfer. Experimental results on the MultiWOZ dataset show that our proposed method significantly improves existing state-of-the-art results in the zero-shot cross-domain setting.