This paper investigates the cooperative moving-target enclosing control problem of networked unicycle-type nonholonomic vehicles with constant linear velocities. The information of the target is only known to some of the vehicles, and the topology of the vehicle network is described by a directed graph. A dynamic control law is proposed to steer the vehicles, such that they can get close to orbiting around the target while the target is moving with a time-vary velocity. Besides, the constraint of bounded angular velocity for the vehicles can always be satisfied. The proposed control law is distributed in the sense that each vehicle only uses its own information and the information of its neighbors in the network. Finally, simulation results of an example validate the effectiveness of the proposed control law.