Upper limbs offer a lot of convenient conditions for human lives, whose health directly affect living standards. If an upper limb occurs motor dysfunction, it has to undergo rehabilitation treatments. For reducing working intensities of physical therapists and improving treatment effects, rehabilitation robots can replace therapists. Ergonomics and kinematic characteristics of elbow joint and shoulder joint were used to design an upper limb rehabilitation robot based on a 3 degree-of-freedom redundant cable-driven parallel mechanism. This rehabilitation robot has a positioning module and a connection module, which is applicable to active therapies and passive therapies with different size upper limbs. Due to the simple structure and assembly, and low manufacturing cost, this robot is easier to be accepted by users. After structure design, the kinematic model of this mechanism was established, and the singularities were analyzed, which were prepared for the follow-up study of motion control. Last, by directly considering force transmission performance and size of this rehabilitation robot, a multi-objective optimal design was implemented. The simulations showed the related performances of this robot was improved effectively by this optimal design. The research results can provide a theoretical reference for the applications of cable-driven parallel mechanisms in design of upper limb rehabilitation robots.