Spatial structures have the different dynamic characteristics from general rahmen structures. Therefore, it is necessary to accurately analyze dynamic characteristics and seismic response for seismic design of spatial structure. Keel arch structure is used as an example structure because it has primary characteristics of spatial structures. In case of spatial structures with different ground condition and time lag, multiple support excitation may be subjected to supports of a keel arch structure. In this study, the response of the keel arch structure under multiple support excitation and with time lag are analyzed by means of the pseudo excitation method. Pseudo excitation method shows that the structural response is divided into two parts, ground displacement and structural dynamic response due to ground motion excitation. It is known that the seismic responses of spatial structure under multiple support excitation are different from those of spatial structure under simple excitation. And the seismic response of spatial structure with time lag are different from those of spatial structure without time lag. Therefore, it has to be necessary to analyze the seismic response of spatial structure under multiple support excitation and time lag because the spatial structure supports may be different and very long span. It is shown that the seismic response of spatial structure under multiple support seismic excitation are different from those of spatial structure under unique excitation.