This paper presents a novel six-degree-of-freedom (6-DOF) parallel platform that is used as the third mirror adjustment system of a large space telescope. In order to meet the design requirements of high precision, a large load–size ratio, and high stiffness in both the transverse and the vertical directions, the parallel platform is designed to be a 6-P-RR-R-RR structure via use of offset RR-joints. The inverse kinematics problem of the designed platform with offset RR-joints is much more complicated than that of a parallel platform with common universal joints owing to the presence of joint-dependent variables in the former problem. In this study, inverse kinematics of the designed parallel platform is mathematically modeled and the Newton–Raphson numerical iterative computation is performed. The accuracy and effectiveness of the proposed mathematical approach are verified by numerical co-simulations using MATLAB and ADAMS. The initial position of the platform is determined by a precision measuring arm. A test system is constructed, and then inverse kinematics solution, resolutions and adjusting steps accuracies of the platform are tested using grating length gauges. Motion strokes of the parallel mechanism are measured using laser tracker.