Robotic-assisted rehabilitation therapy has been shown to be effective in improving upper limb motor function and the daily behavior of patients with motor dysfunction. At present, the majority of upper limb rehabilitation robots can only move in the two-dimensional plane, and cannot adjust the assistance mode in real-time according to the patient’s rehabilitation needs. In this paper, according to the shortcomings of the current rehabilitation robot only moving in the two-dimensional plane, a type of bilateral mirror upper limb rehabilitation robot structure with the healthy side assisting the affected side is proposed. This can move in three-dimensional space. Additionally, an assist-as-needed (AAN) control strategy for upper limb rehabilitation training is proposed based on the bilateral upper limb rehabilitation robot. The control strategy adopts Gaussian Mixture Model (GMM) and impedance controller to maximize the patient’s rehabilitation effect. In the task’s design, there is no need to rely on the assistance of the therapist, only the patients who completed the task independently. GMM guides the rehabilitation robot to provide different assistance for the patients at different task stages and induces the patients to complete the rehabilitation training independently by judging the extent to which the patients can complete the task. Furthermore, in this paper, the effectiveness of the proposed control strategy was verified by three volunteers participating in a two-dimensional task. The experimental results show that the proposed AAN control strategy can effectively provide appropriate assistance according to the classification stage of the interaction between the patients and the rehabilitation robot, and thus, patients can better achieve the rehabilitation effect during the rehabilitation task as much as possible.