The typical hydraulic system of hoist is composed of a hydraulic supply unit, a directional control valve, counter balance valve, and flow control valves. The flow capacity coefficients of flow control valves should be adjusted so that the hoist is operated at moderate speed and the hydraulic energy loss is minimized. However, it is difficult to adjust the flow coefficients of flow control valves by trial and error for optimal operation. Here, the steady state model of the hoist hydraulic system including the differential cylinder circuit is derived and the optimal flow capacity coefficients of flow control valves are obtained using the complex method that is one kind of constrained direct search method.