Improvements can be achieved by incorporating incoming and outgoing adjacent matrices to generate global and local preferences,and directly model the two preferences to build session rep-resentation.However,the incoming matrix and outgoing matrix of a session have no strong rele-vance,and their concatenation may introduce noise for building two preferences.Secondly,the global and local preferences can benefit from each other,and collaborative information of neighbor-hood sessions may help to improve recommendation performance.Therefore,a session-based recom-mendation with preference interaction from separate incoming adjacent matrix and outgoing adjacent matrix framework was proposed,which includes two parallel modules:an incoming session represen-tation encoder(ISE)and an outgoing session representation encoder(OSE).The ISE models ses-sion representation with incoming information through GNN and parallel co-attention mechanism.The OSE models session representation with outcome information through GNN and parallel co-atten-tion mechanism.Finally,a fusion gating mechanism is introduced to balance the importance of ses-sion representations resulting from ISE and OSE.The experimental results show that proposed model obviously outperforms other state-of-the-art methods on Yoochoose and Diginetica datasets.