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Graph neural networks (GNN) have recently been applied to exploit knowledge graph (KG) for recommendation. Existing GNN-based methods explicitly model the dependency between an entity and its local graph context in KG (i.e., the set of its first-order neighbors), but may not be effective in capturing its non-local graph context (i.e., the set of most related high-order neighbors). In this paper, we propose a novel recommendation framework, named Contextualized Graph Attention Network (CGAT), which can explicitly exploit both local and non-local graph context information of an entity in KG. Specifically, CGAT captures the local context information by a user-specific graph attention mechanism, considering a user's personalized preferences on entities. Moreover, CGAT employs a biased random walk sampling process to extract the non-local context of an entity, and utilizes a Recurrent Neural Network (RNN) to model the dependency between the entity and its non-local contextual entities. To capture the user's personalized preferences on items, an item-specific attention mechanism is also developed to model the dependency between a target item and the contextual items extracted from the user's historical behaviors. Experimental results on real datasets demonstrate the effectiveness of CGAT, compared with state-of-the-art KG-based recommendation methods.