Recommender systems are widely used on the Internet as tools for data analysis, processing and discovery. Traditional recommendation algorithms mostly exploit rating information in a simple way while ignoring some hidden information in ratings, thus restricting recommendation performance. This hidden information in ratings, such as similarities between rated items and items unrated by the same user, can unveil the relationships between users and items by using multiple layers to help find the preferences of users. To focus on this hidden information, we propose a new Bayesian Personalized Ranking algorithm based on multiple-layer neighborhoods (BPRN). We divide items into different sets based on the analysis of user-item relevance and give an order for the sets. Then, we use BPRN to obtain the fine-grained order of items in different sets and finally generate a personalized, sorted list for each user. We have used five real-world datasets to test the accuracy of BPRN and compare its performance with state-of-the-art models. Experiments show that our algorithm greatly improves the accuracy of the recommendation results. In addition, our algorithm distinctly alleviates the problems of data sparsity and cold-start users.