This paper investigates the generalized sequential probability ratio test (GSPRT) with multiple sensors. Focusing on the communication-constrained scenario, where sensors transmit one-bit messages to the fusion center, we propose a decentralized GSRPT based on level-triggered sampling scheme (LTS-GSPRT). The proposed LTS-GSPRT amounts to the algorithm where each sensor successively reports the decisions of local GSPRTs to the fusion center. Interestingly, with significantly lower communication overhead, LTS-GSPRT preserves the same asymptotic performance of the centralized GSPRT as the local thresholds and global thresholds grow large at different rates.