Traditional recommender systems only utilize a single user-item interaction behavior as the optimization target behavior. However, multi-behavior recommender systems leverage multiple user behaviors as auxiliary behaviors(favorite and page view), which is more practical. Therefore, recommender systems by exploring patterns of multiple behaviors are of great significance in improving performance. Many previous works toward multi-behavior recommendation fail to capture user preference intensity for different items in the heterogeneous graph. Meanwhile, they also ignore high-order relationships that incorporate user different preference intensity into user-item heterogeneous interactions. To solve the above challenges, we propose a novel multi-behavior recommendation model named neighbor-aware attention-based heterogeneous relation network model in E-commerce recommendation (NAH). NAH leverages the attention propagation layer to capture user preference intensity for different items and employs a composition method to incorporate relation embeddings into node embeddings for high-order propagation. Experiment results on two real-world datasets verify the effectiveness of our model in the multi-behavior task by comparing it with some start-of-the-art methods. Further studies verify that our model has a significant effect on exploring high-order information and cold-start users who have few user-item interaction records. [ABSTRACT FROM AUTHOR]