This paper proposes an efficient event delivery algorithm called distributed group mobility adaptive event delivery (GMED) for delay tolerant mobile sensor networks (DTMSN). GMED is designed to establish a group-based event delivery model by effectively finding and utilizing the groups generated by moving sensor nodes which then lead an improved performance: On one hand, Inter-Group delivery will be achieved by multi-replica delivery based on its delivery probability to the sink. On the other hand, Intra-Group delivery will be performed by single-replica delivery through established transmission paths because each node have stable neighbor sets inside group. Meanwhile, delivery prioritizing will be based on event priority in the queue. Furthermore, a redundant replica control mechanism is also introduced to optimize replica management and network overload. Simulation results have shown that GMED not only achieves a relatively long network lifetime, but also has a higher message delivery ratio at lower transmission overhead and delay than other DTMSN data delivering approaches.