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Session-based recommendation (SBR) is a challenging task, which aims at recommending items based on anonymous behavior sequences. Most existing SBR studies model the user preferences based only on the current session while neglecting the item-transition information from the other sessions, which suffer from the inability of modeling the complicated item-transition pattern. To address the limitations, we introduce global item-transition information to strength the modeling of the dynamic item-transition. For fully exploiting the global item-transition information, two ways of exploring global information for SBR are studied in this work. Specifically, we first propose a basic GNN-based framework (BGNN), which solely uses session-level item-transition information on session graph. Based on BGNN, we propose a novel approach, called Session-based Recommendation with Global Information (SRGI), which infers the user preferences via fully exploring 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 (ii) Constrained-based Model (SRGI-CM), which treats the global-level item-transition information as a constraint to ensure the learned item embeddings are consistent with the global item-transition. Extensive experiments conducted on three popular benchmark datasets demonstrate that both SRGI-FM and SRGI-CM outperform the state-of-the-art methods consistently.