A mobile satellite communication system (MSCS) is a device installed on a moving carrier for mobile satellite communication. It can eliminate disturbance and maintain continuous satellite communication when the carrier is moving. Because of many advantages of mobile satellite communication, the MSCSs are becoming more and more popular in modern mobile communication. In this paper, a typical ship-mounted MSCS is studied. The dynamic model of the system is derived using the generalized Lagrange method both in the joint space and in the workspace. Based on the dynamic model, a nonlinear computed torque controller with trajectory planning is designed to track an aimed satellite with a satisfied transient response. Simulation results in two different situations are presented to show the tracking performance of the controller.