Recommender systems have been demonstrated to be effective to meet user's personalized interests for many online services (e.g., E-commerce and online advertising platforms). Recent years have witnessed the emerging success of many deep learning-based recommendation models for augmenting collaborative filtering architectures with various neural network architectures, such as multi-layer perceptron and autoencoder. However, the majority of them model the user-item relationship with single type of interaction, while overlooking the diversity of user behaviors on interacting with items, which can be click, add-to-cart, tag-as-favorite and purchase. Such various types of interaction behaviors have great potential in providing rich information for understanding the user preferences. In this paper, we pay special attention on user-item relationships with the exploration of multi-typed user behaviors. Technically, we contribute a new multi-behavior graph neural network (MBRec), which specially accounts for diverse interaction patterns as well as the underlying cross-type behavior inter-dependencies. In the MBRec framework, we develop a graph-structured learning framework to perform expressive modeling of high-order connectivity in behavior-aware user-item interaction graph. After that, a mutual relation encoder is proposed to adaptively uncover complex relational structures and make aggregations across layer-specific behavior representations. Through comprehensive evaluation on real-world datasets, the advantages of our MBRec method have been validated under different experimental settings. Further analysis verifies the positive effects of incorporating the multi-behavioral context into the recommendation paradigm. Additionally, the conducted case studies offer insights into the interpretability of user multi-behavior representations.