This paper proposes an analytical approach to solve inverse kinematics of 6-DOF manipulators. Since the manipulator discussed here is designed with the S-RRR configuration, it is difficult to solve the inverse kinematics analytically. So, the reverse coordinates method is developed. This paper obtains a new 6-DOF manipulator with RRR-S configuration by inverting the base and the end effector of the manipulator. Then, analysis of inverse kinematics for the new manipulator is presented. According to the relationship of joints between the original and the new manipulators, the solutions of inverse kinematics for the original manipulator are completed. Besides, the evaluation criteria of all feasible inverse kinematic solutions with joint limits are established. And finally, the validity of the method is verified by kinematic simulations.