The positioning accuracy of industrial robots has an important influence on the stability and accuracy of robotic motion, which is one of the important indexes to measure the performance of robots. At present, some probability theory based methods are used to evaluate the positioning accuracy reliability of industrial robots. In practical engineering, the precise probability distribution of some robot’s parameters cannot be obtained directly. This study first uses the aleatory-epistemic hybrid model to describe the uncertain parameters of industrial robots. Second, the uncertain parameters are considered to construct the kinematic equation of industrial robots. Third, a probability-evidence hybrid reliability analysis model of industrial robots is established. Finally, the reliability interval of industrial robots under different thresholds can be obtained. Compared with the traditional method, the reliability results of industrial robots obtained by this method is an interval, which can more objectively evaluate the kinematics reliability of industrial robots. In the example, the effectiveness of the proposed method is verified by a six degrees of freedom (6-DoF) industrial robot.