A six degrees of freedom (6-DOF) medical positioning robot is designed according to the demands for heavy ion accurate radiotherapy in treatment room with fixed beam, the structure scheme is proposed and a virtual prototype model is established. In order to avoid the defects in the kinematics modeling of robots using the traditional Denavit-Hartenberg (D-H) parameter method, a method for kinematics modeling of the medical positioning robot was introduced based on the Special Euclidean Group of Lie group rigid motion and screw theory. On this basis, the mechanism collision interference, the workspace and the beam irradiation range of the positioning robot were investigated with simulation. The results show that the designed 6-DOF medical positioning robot can meet the conditions of accurate movement and positioning in continuous space, and can well meet the needs of multi-directional beam irradiation in a large range.