This paper proposes the finite-time circumnavigation controller with torque input for multiple nonholonomic mobile robots to track and circle moving targets. By comprehensively considering the robots’ kinematic and dynamic models, the control system is divided into two layers. At the kinematic level, appropriate linear and angular velocities are generated by constructing relative velocity and employing dynamic feedback linearization. At the dynamic level, error vectors are redefined, and a new error model is derived. A finite-time circumnavigation controller with torque input is designed using backstepping to track trajectories generated at the kinematic level. Additionally, a compensation term is introduced in the controller design to mitigate disturbances. Furthermore, simulations confirm the efficacy of the controller proposed.