Powered exoskeleton rehabilitation is an effective way to help stroke patients recover their motor abilities. Bionic structures and human-like control strategies can be used to enhance both the safety and efficacy of exoskeletons. However, the motion characteristics of the shoulder complex are not sufficiently considered. In this paper, we designed a 7-degrees-of-freedom (DOF) upper limb rehabilitation exoskeleton, FREE (functional rehabilitation exoskeleton). The mechanical structures of the shoulder and forearm of FREE are in accordance with human anatomy, and can be used to perform a wide range of synergistic motion of multiple joints while keeping a safe distance from the patient’s head. A multiple-input-multiple-output (MIMO) shoulder girdle motion prediction model was developed to satisfy the synergy between humans and exoskeletons. Moreover, a constrained task priority and projected gradient-based inverse kinematics algorithm (CTPPG-IK) was proposed to achieve assistance with scapulohumeral rhythm. A motion capture system was used to collect different activities of daily life (ADL) motion data to validate the proposed algorithm. The experimental results show that the accuracy of the prediction model is higher than that of existing models, and the inverse kinematics algorithm can handle the end-effector task and joint space with a maximum angle error of 3.04×10−3 rad.