In this study， the trajectory tracking and obstacle avoidance of redundant robotic manipulators are unified as an optimization problem， and a trajectory-tracking optimizer with obstacle avoidance capability based on an improved grey wolf optimizer （IGWO） is proposed. First， the obstacle avoidance space is modeled using the bounding box method， and the GJK algorithm is used to calculate the minimum distance between the robotic manipulator and the obstacle. Second， a fitness function is derived， and a reward function for obstacle avoidance is introduced to actively reward the optimizer such that the manipulator can track the target trajectory while avoiding obstacles. Third， the grey wolf optimizer （GWO） is improved using a random dispersion strategy to improve its global search ability and solve optimization problems more accurately. Finally， the effectiveness and superiority of the proposed method were verified using a nine-degree-of-freedom redundant robotic manipulator. The experimental results show that for a circular target trajectory， the tracking error of the robotic manipulator is 0.21 mm. During the tracking process， the distance between the robotic manipulator and obstacle is not shorter than 70 mm. Compared to the GWO， the IGWO improved the tracking accuracy by 13%. The proposed trajectory tracking optimizer can perform the trajectory tracking and obstacle avoidance tasks of redundant robotic manipulators with millimeter-level accuracy； the IGWO can effectively improve the convergence accuracy of the classical GWO.