To investigate the non-linear vibration behavior of spatial inclined cables subjected to harmonic displacement excitation at beam end or tower end, based on Newton's laws of motion and the tension forces of cable, the three-dimensional non-linear coupling control oscillatory differential equations in loosening and non-loosening state with the arbitrary direction excitations are derived. Runge-Kutta subsection integration method is applied to obtain those equations. The research results show that the cable will present coupled vibration characteristic of the out-of-plane and in-plane in three-dimensional spatial coordinates, the coupled vibration amplitude is relation with the matching ratio of natural frequencies of cable and excitation frequencies; in in-plane displacement excitation, the out-of-plane auto-parametric vibration will be found by increasing the excitation amplitude; with the accretion of the initial sag and the excitation amplitude, the alternate variation processes between loosening and non-loosening state are exposed during cable vibrations.