The 7-DOF redundant manipulator in greatly improves the obstacle/singularity avoidance capability and operational flexibility. Meanwhile, its inverse kinematics problem would be much difficult since 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. Simulations show that this method has high commonality, no special structure of robot required, and also has improved computational efficiency and reliability.