The robot-assisted therapy has been demonstrated to be effective in the improvements of limb function and even activities of daily living for patients after stroke. This paper presents an interactive upper-limb rehabilitation robot with a parallel mechanism and an isometric screen embedded in the platform to display trajectories. In the dynamic modeling for impedance control, the effects of friction and inertia are reduced by introducing the principle of virtual work and derivative of Jacobian matrix. To achieve the assist-as-needed impedance control for arbitrary trajectories, the strategy based on orthogonal deviations is proposed. Simulations and experiments were performed to validate the dynamic modeling and impedance control. Besides, to investigate the influence of the impedance in practice, a subject participated in experiments and performed two types of movements with the robot, that is, rectilinear and circular movements, under four conditions, that is, with/without resistance or impedance, respectively. The results showed that the impedance and resistance affected both mean absolute error and standard deviation of movements and also demonstrated the significant differences between movements with/without impedance and resistance (p < 0.001). Furthermore, the error patterns were discussed, which suggested that the impedance environment was capable of alleviating movement deviations by compensating the synergetic inadequacy between the shoulder and elbow joints.