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