Multi-hop path reasoning over knowledge base aims at finding answer entities for an input question by walking along a path of triples from graph structure data, which is a crucial branch in the knowledge base question answering (KBQA) research field. Previous studies rely on deep neural networks to simulate the way humans solve multi-hop questions, which do not consider the latent relation information contained in connected edges, and lack of measuring the correlation between specific relations and the input question. To address these challenges, we propose an edge-aware graph neural network for multi-hop path reasoning task. First, a query node is directly added to the candidate subgraph retrieved from the knowledge base, which constructs what we term a query graph. This graph construction strategy makes it possible to enhance the information flow between the question and the nodes for the subsequent message passing steps. Second, question-related information contained in the relations is added to the entity node representations during graph updating; meanwhile, the relation representations are updated. Finally, the attention mechanism is used to weight the contribution from neighbor nodes so that only the information of neighbor nodes related to the query can be injected into new node representations. Experimental results on MetaQA and PathQuestion-Large (PQL) benchmarks demonstrate that the proposed model achieves higher Hit@1 and F1 scores than the baseline methods by a large margin. Moreover, ablation studies show that both the graph construction and the graph update algorithm contribute to performance improvement.