This paper presents a synergy pursuit strategy that multiple underwater robots pursue a single moving target based on finite state machine. The processes of the pursuit are defined as seven different states, and to implement each state, the corresponding strategies are designed. As the strategy for each state is implemented by a corresponding formation control, a synergy control law is also designed for multiple underwater robots. In the design of the pursuit strategy, the definition of encirclement is put forward for the underwater robots. Furthermore, the proof that a point is encircled by other points on the plane is given. To solve the problem of the concealment in the tracking and the pursuit, a semicircular pursuit strategy and a circular pursuit strategy are also proposed. Finally, based on this pursuit strategy, the simulation of whole process is carried out with the MOOS(Mission Oriented Operating Suite) platform, and the effectiveness of the semicircular and circular pursuit strategy are verified by lake experiment with practical robots. The results of simulation and lake experiment prove that this pursuit strategy can realize synergy tracking and pursuit for a single moving target under the given conditions.