This paper presents a fully distributed algorithm for target tracking using a mobile sensor network. It tries to maintain the target being visible to the mobile network all the time while consuming as little motion energy as possible. Meanwhile the network connectivity is maintained. At every time, only the nodes around the target are activated while other nodes keep idle. Certain functions are defined to quantify the main aspects in the tracking such as the target escaping probability and the network connectivity status. They transform the tracking into a multi-objective optimization problem. To solve this global problem, a local motion strategy is proposed. Simulation results show that our algorithm yields good performance.