A numerical model is constructed for carrying out the nonlinear random vibrations of 3D floating structures moored by cables under seismic and wave excitations. The floating structure is moored to the seabed by four cables that distribute symmetrically around the floating structure. The 3D nonlinear elementary stiffness matrix of cable, rather than the tangent elementary stiffness matrix of cable, is derived based on the extended Hamilton principle. The nonlinear equations of motions of the mooring cables are formulated using the 3D cable elements. The floating platform is modeled as a rigid body with six degrees of freedom. The effects of added mass and nonlinear hydrodynamic drag forces for both the floating platform and mooring cables are taken into consideration. The connection conditions which represent the relationships between the displacements of the floating platform and cables are formulated. The equations of motions of both the mooring cables and floating platform are formulated separately and then assembled as a whole system through the connection conditions. Eventually, the whole system under both horizontal seismic ground motion and wave excitation is analyzed numerically using Monte Carlo simulation method. The mean values, standard deviations and probability density functions of the responses of the floating structure and the maximum tensile force in the cables are presented and studied under various conditions.