Session-based recommendation aims to predict the next interaction item for anonymous users based on short-term interaction data. Most of the existing graph neural network session recommendation models treat all neighboring nodes equally during information propagation without distinguishing their importance to the central node, which introduces noise into the model training. In addition, the problem of over-smoothing arises as the number of layers of graph neural networks increases. To address these issues, a model named multi-layer graph attention network with skip connection for session-based recommendation (MGATSC) is proposed. Firstly, the graph attention network is used to learn the importance of neighboring nodes to the central node, and multiple networks are stacked to obtain high-order neighbor information. Then, to alleviate the over-smoothing problem, a skip connection based on the residual attention mechanism is used to update the node embeddings of each network layer, and the final node embedding is obtained through average pooling. Finally, the reverse positional embedding is fused into the node embedding, and recommendations are generated through the prediction layer. Experimental results on three public datasets, Tmall, Diginetica, and Retailrocket, demonstrate that the proposed model outperforms all baseline models, which validates the effectiveness and rationality of the model.