Aiming at the problem that it is difficult for the existing session-based recommendation models to explicitly express the influence of items on the recommendation results， a Session-based Recommendation model by graph neural network fused with Item Influence （SR-II） was proposed. Firstly， a new edge weight calculation method was proposed to construct a graph structure， in which the calculated result was used as the influence weight of the transition relationship in the graph， and the features of the graph were extracted through the influence graph gated layer by using Graph Neural Network （GNN）. Then， an improved shortcut graph was proposed to connect related items， effectively capture long-range dependencies， and enrich the information expressed by the graph structure； and the features of the graph were extracted through the shortcut graph attention layer by using the attention mechanism. Finally， a recommendation model was constructed by combining the above two layers. In the experimental results on Diginetica and Gowalla datasets， the highest HR@20 of SR-II is reaching 53.12%， and the highest MRR@20 of SR-II is reaching 25.79%. On Diginetica dataset， compared with CORE-trm （simple and effective session-based recommendation within COnsistent REpresentation space-transformer）， SR-II has the HR@20 improved by 1.10% ，and the MRR@20 improved by 1.21%； On Gowalla dataset， compared with SR-SAN（Session-based Recommendation with Self-Attention Networks）， SR-II has the HR@20 improved by 1.73%.Compared with the recommendation model called LESSR （Lossless Edge-order preserving aggregation and Shortcut graph attention for Session-based Recommendation）， SR-II has the MRR@20 improved by 1.14%. The experimental results show that the performance of SR-II is better than that of the comparison models， and SR-II has a higher recommendation accuracy.