To meet the special requirements of the third mirror adjustment system for an optical telescope, a 6-P-RR-R-RR parallel platform using offset RR-joints is designed with high precision, a large load-to-size ratio and high stiffness. In order to improve the adjustment accuracy and the stiffness of the whole mechanism, each rotating joint in the subchain is designed as a zero-gap bead shaft system. When compared with a traditional Hooke joint, the offset RR joint has certain characteristics, including large carrying capacity and easy processing and adjustment, that effectively reduce the risk of interference with the joint during rotation and increase the working space of the entire machine. Because of the additional variables introduced by the offset joints, the kinematics problem becomes much more complicated. Regarding the P-RRRRR series subchain, the kinematics model is established using the Denavit–Hartenberg parameter method and then solved by the numerical iteration method. The stiffness of the parallel platform is analyzed and tested, including static and fundamental frequency. Motion performance testing of the parallel platform is performed.