The nonlinear oscillations of the floating structures anchored by cables are studied in three dimensions. The floating structure is anchored by four symmetric mooring lines and the mooring lines are fixed on the seafloor at the other ends. The stiffness matrix of 3D cable element has been established and applied to analyze the dynamics of the 3D floating structures anchored by cables. The complex compatibility conditions which relate the responses of the floating body and cables have been proposed. The equations of motion for the mooring lines and floating body are individually formulated. Then they are combined as an entire system by utilizing the compatibility conditions. At last, the entire system is analyzed numerically with horizontal harmonic excitations applied on the floating body. The amplitudes for both the responses of the platform and the maximum mooring force are studied as the excitation frequency changes. The responses of the platform and the maximum mooring force are also investigated for varieties of cable parameters.