Abstract: The non-stationary random seismic analysis of long-span spatial structures under multi-support excitations of three-dimensional orthogonal earthquake motion was performed. A method for seismic analysis of the multi-support excitations under the three-dimensional non-stationary random earthquake motion was established, and a simplified calculation for the long-span spatial structures was carried out with the wave-front method. The seismic responses of the roof structure of the Tianjin Olympic Center Stadium subject to the uniform excitation, the traveling-wave excitation, and the multi-support excitation considering the partial coherence effect and the seismic nonstationarity, under one-dimensional and three-dimensional random earthquake motions were numerically simulated. The results show that the axial forces of the control bars may be increased by about 30% when considering the three-dimensional effect of earthquake motion, or changed by about 10% when considering the partial coherence, or increased by about 15% when considering the three-dimensional earthquake excitation, or decreased by about 35% when considering the nonstationarity of earthquake motion. A conclusion was given that the multi-support and multi-dimensional earthquake excitations must be considered in the seismic analysis of the long-span spatial structures, and the seismic design is secure when the nonstationarity of earthquake motion is not considered.