Abstract: Recommender systems play an increasingly important role in a wide variety of applications to help users find favorite products. Collaborative filtering has remarkable success in terms of accuracy and becomes one of the most popular recommendation methods. However, these methods have shown unpretentious performance in terms of novelty, diversity, and coverage. We propose a novel graph-based collaborative filtering method, namely Positive Multi-Layer Graph-Based Recommender System (PMLG-RS). PMLG-RS involves a positive multi-layer graph and a path search algorithm to generate recommendations. The positive multi-layer graph consists of two connected layers: the user and item layers. PMLG-RS requires developing a new path search method that finds the shortest path with the highest cost from a source node to every other node. A set of experiments are conducted to compare the PMLG-RS with well-known recommendation methods based on three benchmark datasets, MovieLens-100K, MovieLens-Last, and Film Trust. The results demonstrate the superiority of PMLG-RS and its high capability in making relevant, novel, and diverse recommendations for users.