This paper proposes a new approach named Multi-Preview Control that is developed from Single-Preview Control to achieve an on-line control of trajectory tracking and obstacle avoidance for redundant manipulators effectively without predefined working object's shape. In the trajectory tracking process, the manipulator is required to keep a configuration with maximal avoidance manipulability in real-time. Multi-Preview Control uses several future optimal configurations to control current configuration to complete task of trajectory tracking and obstacle avoidance on-line with higher avoidance manipulability and reachability. In addition, we analyze the relationship between distribution of AMSI(Avoidance Manipulability Shape Index) and shape of manipulator. We verify the effectiveness and validity of Multi-Preview Control through simulations and experiments.