The 7 degrees of freedom (DOF) redundant manipulator greatly improves obstacle/singularity avoidance capability and operational flexibility. However, the inverse kinematics problem of this manipulator is very difficult to solve because it has an infinite number of solutions. This paper uses a new numerical sequence processing method with a closed-loop framework to solve the inverse kinematics of the 7-DOF redundant manipulator. Simulation and experiment show that this method has high commonality. No special structure of the robot is required, and this method has improved computational efficiency and reliability.