An overhead crane system which transports an object by girder motion, trolley motion, and hoist motion becomes a nonlinear system because the length of a rope changes. To develope the position control algorithm for the nonlinear crane systems, we apply a nonlinear optimal control method which uses forward and backward difference methods and obtain optimal inputs. This method is suitable for the overhead crane system which is characterized by the differential equation of higher degree and swing motion. From the results of computer simulation, it is founded that the position of the overhead crane system is controlled, and the swing of the object is suppressed.