In this paper, an energy-efficient technique is proposed for tracking a target in a field using a network of mobile sensors while maximizing the life span of the network. The most important energy consumption sources in a mobile sensor network (MSN) are sensing, communication and movement of the sensors. In the proposed technique, first the field is divided into a grid of arbitrarily small cells. This grid is then used to obtain a graph with properly weighted edges. The weight assignment is done in such a way that it results in a close estimate of the maximum lifetime for the network. Finally, using a shortest path algorithm, an efficient route is found to transfer information from the target to destination.