This paper proposes and analyses an approach named predictive control of redundant manipulators based on Avoidance Manipulability Shape Index with Potential (AMSIP), which is an evaluation index considering avoidance manipulability and collision possibility, in order to achieve an on-line control of trajectory tracking and obstacle avoidance for redundant manipulators. In the trajectory tracking process, manipulator is required to keep a configuration with maximal avoidance manipulability in real time. Predictive control in this paper uses manipulators' future configurations to control current configuration aiming at completing tasks of trajectory tracking and obstacle avoidance on-line and simultaneously with higher avoidance manipulability. We compare Multi-Preview Control with Predictive Control using redundant manipulator, and show the results through simulations. Moreover, we validate the effectiveness of Predictive Control through AMSIP distribution.