This paper deals with the nonlinear effect of the drift motion of multi-chain mooring buoys. The buoy’s motion in time domain is determined for the case that the wave and mooring force are nonlinear. The Kotorayama’s method of hydrodynamic effect in a single mooring chain is expanded to multi-mooring chains. The time history of drift motion of the mooring buoy in regular waves and wave groups is calculated. The relation between the drift motion and the wave height or difference frequency is discussed. It can be shown that the effect of the hydrodynamic force acting on the mooring chain has remarkable influence on the total drift motion of the mooring buoy. In a wave group, its amplitude is mainly controled by the wave height and has little relation with difference frequency. This paper deals with the nonlinear effect of the drift motion of multi-chain mooring buoys. The buoy’s motion in time domain is determined for the case that the wave and mooring force are nonlinear. The Kotorayama’s method of hydrodynamic effect in a single mooring chain is The time history of drift motion of the mooring buoy in regular waves and wave groups is calculated. The relation between the drift motion and the wave height or difference frequency is discussed. It can be shown that the effect of the hydrodynamic force acting on the mooring chain has remarkable influence on the total drift motion of the mooring buoy.