In this paper, an enclosing control problem is investigated for nonholonomic mobile agents with a moving target of unknown velocity. An adaptive observer containing two internal variables is first designed for each agent to compensate for the lack of the target velocity information. One variable is designed to estimate the unknown target velocity and further its estimation error is assessed by the other internal variable to subsequently guarantee the control performance. Then using the estimated information from the adaptive observer, a dynamic control law for circular formation of nonholonomic agents around the moving target is designed by a backstepping process. The global asymptotical stability of the closed-loop system is achieved under the proposed dynamic control law with the adaptive observer. Finally, a simulation is conducted to demonstrate the effectiveness of the proposed approach.