Abstract: The time history analytical model under multi-support excitations is established based on the direct displacement input method. Non-stationary spatial ground motions are generated by trigonometric series method, which are compatible with the given coherence loss function and code response spectrum. The long-span spatial truss structure supported by columns is considered, and the dynamic responses of the structure under uniform excitation, wave-passage excitation and multi-support excitations are investigated comparatively. In contrast to the uniform excitation, under horizontal multi-support excitations, the internal force responses of the supporting columns which are first excited by seismic waves are amplified, the amplification of both the column-top displacements and the axial forces of control bars in the superstructure are related with the direction of seismic excitation. The seismic responses of the structure under vertical multi-support excitations are larger than those under vertical uniform excitations. The variations of the analytical results under multi-support excitations of the truss structure are close to those under the wave-passage excitation, but the response results obtained from the wave-passage excitation are unreliable in most cases. Therefore, neglecting ground motion spatial variations may lead to a substantially under-estimated seismic response of long-span spatial truss structure.