When a FPSO (Floating Production Storage and Offloading) is required to maintain the specified position during oil producing and offloading under the external forces such as ocean current, wind or wave, exact position measurement is firstly taken into consideration. GPS (Global Positioning System) is mainly used to measure ship's position. But the position measurements using GPS contain noise. This noise has large influence on DPS (Dynamic Positioning System), therefore it is necessary to remove the noise. In this paper, Inverse Linear Quadratic (ILQ) optimal servo theory using Kalman filter is applied to design control system of DPS. Generally, Kalman filter is to estimate the low-frequency motions of the vessel so that control can be applied to minimise the position error. But in this paper, Because we already consider motion of FPSO as low-frequency motion, Kalman filter is used to remove the measurement noise. The numerical simulations shows the performance of the combined Kalman filter and ILQ optimal servo system.