This paper mainly focuses on the trajectory tracking control of a lower extremity rehabilitation robot during passive training process of patients. Firstly, a mathematical model of the rehabilitation robot is introduced by using Lagrangian analysis. Then, a model based computed-torque control scheme is designed to control the constrained four-link robot (with patient's foot fixed on robot's end-effector) to track a predefined trajectory. Simulation results are provided to illustrate the effectiveness of the proposed model based computed-torque algorithm. In the simulation, a multi-body dynamics and motion software named ADAMS is used. The combined simulation of ADAMS and MATLAB is able to produce more realistic results of this complex integrated system.