The nonlinear vibrations of the moored floating structures under horizontal sinusoidal excitations are studied in three dimensions. Four mooring lines are connected to the floating structure and fixed to the sea bed. The nonlinear equations of motions of the mooring lines are formulated using the cable elements formulated based on the extended Hamilton principle. The floating structure is considered as a rigid body with six degrees of freedom. Then the equations of motion of the floating structure and mooring lines are formulated through their connection conditions. In the last, the equations of motion of the whole structure are analyzed numerically. The influences of different sag-to-span ratio and inclined angle of the mooring cables on the responses of the floating structure are studied. The response amplitudes of the moored floating structure are also studied as the external frequency changes.