To assist stroke patients with rehabilitation training, an upper limb rehabilitation robot with an exoskeleton structure and three degrees of freedom (DOF) was developed in this paper. Under the guidance of the theory of rehabilitation medicine, the mechanical design of the robot was completed. Then, the kinematics equations were established by means of homogeneous transformation, including the forward kinematics and the inverse kinematics. The kinematical analysis was carried out and the algebraic solution of inverse kinematics was derived, which provided a theoretical basis for realizing the intelligent control. To validate the performance, the kinematical simulation was conducted, and the simulation results showed that the design of the exoskeleton robot was feasible.