This paper proposes and analyses an approach named predictive control of redundant manipulators based on avoidance manipulability 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 first order prediction with second order prediction and show the results through simulation. Moreover, we validate the effectiveness of predictive control through Avoidance Manipulability Shape Index with Potential (AMSIP) distribution.