In this paper, mechanical design and control of an exoskeleton robot for shoulder rehabilitation after stroke are presented. Initially, mechanical design of a new 3 degrees of freedom (DOF) exoskeleton robot for shoulder joint rehabilitation is presented. All robot measurements are based on the properties of upper limb of an adult person. A new open circular mechanism is proposed for the third joint. Afterwards, direct and inverse kinematics, Jacobian matrix, singular points, and dynamics of the robot are presented. In order to study the ability of the robot to follow the optimized trajectories, sliding mode controller (SMC) is proposed to track desired trajectories. In most rehabilitation robots, the attention is on robot’s mechanical design, so linear controllers are used to control the robot. However, rehabilitation robots are non-linear in nature and non-linear control methods are required that can reject uncertainties and are resistant to parameter changes. SMC is robust due to its nonlinear nature, and can reject uncertainties and disturbances applying on the system such as patient’s hand tremor. The parameters of the SMC are tuned using Genetic Algorithm (GA). The main advantage of this robot compared to similar systems are being low weight, having a special mechanism for third joint that solves the known issues associated with long wiring and closed mechanisms, allowing translational degrees of freedom of the shoulder, ease of use, comfort for the patient and the tracking performance of the controllers.