There is increasing interest in using rehabilitation robots to assist post-stroke patients during rehabilitation therapy. The motion control of the robot plays an important role in the process of functional recovery training. Due to the change of the arm impedance of the post-stroke patient in the passive recovery training, the conventional motion control based on a proportional-integral (PI) controller is difficult to produce smooth movement of the robot to track the designed trajectory set by the rehabilitation therapist. In this paper, we model the dynamics of post-stroke patient arm as an impedance model, and propose an adaptive control scheme, which consists of an adaptive PI control algorithm and an adaptive damping control algorithm, to control the rehabilitation robot moving along predefined trajectories stably and smoothly. An equivalent two-port circuit of the rehabilitation robot and human arm is built, and the passivity theory of circuits is used to analyze the stability and smoothness performance of the robot. A slide Least Mean Square with adaptive window (SLMS-AW) method is presented for on-line estimation of the parameters of the arm impedance model, which is used for adjusting the gains of the PI-damping controller. In this paper, the Barrett WAM Arm manipulator is used as the main hardware platform for the functional recovery training of the post-stroke patient. Passive recovery training has been implemented on the WAM Arm, and the experimental results demonstrate the effectiveness and potential of the proposed adaptive control strategies.