Recommendation systems provide personalized service to users and aim at suggesting to them items that they may prefer. There is an increasing requirement of next-item recommendation systems to infer a user's next favor item based on his/her historical selection of items. In this paper, we study the next-item recommendation under the cold-start situation, where the users in the system share no interaction with the new items. Specifically, we seek to address the problem from the perspective of zero-shot learning (ZSL), which classifies samples whose classes are unseen during training. To this end, we crystallize the relationship and setting from ZSL to cold-start next-item recommendation, and further propose a novel model called User-Item Matching and Auto-encoders (UIMA) which learns the latent embeddings for both users and items by exploiting user historical preferences and item attributes. Concretely, UIMA consists of three components, i.e., two auto-encoders for learning user and item embeddings and a matching network to explore the relationship between the learned user and item embeddings. We perform experiments on several cold-start next-item recommendation datasets, including movies, music, and bookmarks. Promising results demonstrate the effectiveness of the proposed method for cold-start next-item recommendation.