Session-based recommendation focuses on predicting the next item a user will interact with based on sequences of anonymous user sessions. A significant challenge in this field is data sparsity due to the typically short-term interactions. Most existing methods rely heavily on users' current interactions, overlooking the wealth of auxiliary information available. To address this, we propose a novel model, the Multi-Graph Co-Training model (MGCOT), which leverages not only the current session graph but also similar session graphs and a global item relation graph. This approach allows for a more comprehensive exploration of intrinsic relationships and better captures user intent from multiple views, enabling session representations to complement each other. Additionally, MGCOT employs multi-head attention mechanisms to effectively capture relevant session intent and uses contrastive learning to form accurate and robust session representations. Extensive experiments on three datasets demonstrate that MGCOT significantly enhances the performance of session-based recommendations, particularly on the Diginetica dataset, achieving improvements up to 2.00% in P@20 and 10.70% in MRR@20. Resources have been made publicly available in our GitHub repository https://github.com/liang-tian-tian/MGCOT.