Based on the three-dimensional linear potential flow theory and the three-dimensional finite water depth Green function method, the hydrodynamic analysis of a new offshore leisure platform is conducted. The Response Amplitude Operator (RAO) when the water depth of the platform is 20 m is calculated, and the natural characteristics and wave response of the platform in shallow water environment are obtained. Taken into account the combined effect of wind, wave, and current, three mooring schemes are designed to conduct the time domain analysis in coupled motion of mooring system of the platform. The comparative analyses in mooring tension, bottoming, and air gap are conducted to select the better mooring scheme. The analysis results are of certain reference significance for the mooring design of shallow water floating platform.