Since multi-hop mobile ad hoc network (MANET) contains a set of wireless mobile nodes forming a temporary network, the topology is strongly influenced by the node mobility models. Numerous mobility models have been presented, including the Random Waypoint Mobility Model (RWMM), Manhattan Grid Mobility Model (MGMM), Freeway Mobility Model (FMM), and so on. In MGMM, the trajectories of mobile nodes are confined to a grid topology. MGMM is an important mobility model, and numerous objects following MGMM can be enumerated, such as the movement of cars in the city, the movement of people though department stores etc. The expected link life time (ELLT) is an important performance parameter in MANET. When a node wishes to transmit information to the other node directly, these two nodes must be within each other's transmission range for a period of time. This period is called the link life time (LLT). The ELLT is the expected value of LLT. The goal of this work largely focuses on identifying the ELLT of the MANET under MGMM by using mathematical analysis. Based on our observation, two nodes involved in constructing a connection under MGMM can be classified into three independent cases: namely parallel with opposite directions, parallel with same directions, and vertical cases. These three cases can be formulated independently. To verify these formulations numerous simulations are done by ns2, and the theoretical and simulation results are well matched.