Graph Neural Networks (GNNs) have advanced graph representation learning, with Graph Isomorphism Network (GIN) standing out for its strong expressiveness. However, GIN relies only on local neighborhoods for feature aggregation, which makes it difficult to model global structural information effectively, and the fixed neighborhoods limit the information propagation range, which affects the model performance. To solve this problem, this paper proposes a novel GIN model-Hybrid Neighborhood and Double Layer Attention Mechanism Based Graph Isomorphism Network (HG-GIN). HG-GIN combines direct edges relying on local neighborhoods and hidden edges obtained through global similarity information to optimize the aggregation of domain information, and proposes a double layer attention mechanism. We extensively evaluate HG-GIN on different graph benchmark datasets and observe its superior performance over other state-of-the-art GNN methods on several graph classification tasks. HG-GIN considers the role of neighbors and optimizes the neighborhood distribution, and the experimental results show that the proposed HG-GIN achieves state-of-the-art performance on a variety of open graph datasets.