Session-based recommendation (SBR) is a challenging task, which aims at recommending items based on anonymous behavior sequences. Almost all existing SBR studies model user preferences only based on the current session while neglecting the global item-transition information from the other sessions. Specifically, we first propose a basic GNN-based session recommendation model on SBR problem by solely using session-level item-transition information on session graph. Then, we also propose a novel approach, called Session-based Recommendation with Global Information (SRGI), which infers the user preferences of the current session via fully exploiting global item-transitions over all sessions from two different perspectives: (i) Fusion-based Model (SRGI-FM), which recursively incorporates the neighbor embeddings of each node on global graph into the learning process of session-level item representation; and (b) Constrained-based model SRGI-CM, which treats the global-level item-transition information as a constraint to ensure the learnt item embeddings are consistent with the graph structure. Extensive experiments conduct on three popular benchmark datasets demonstrates that both (SRGI-FM) and (SRGI-CM) outperform the state-of-the-art methods consistently.