The current research on ground motion parameters and fragility analysis of large-span spatial reticulated domes mostly focuses on the superstructure, ignoring the influence of the substructures on the overall structure. In order to select the ground motion parameters suitable for evaluating the response of schwedler single-layer reticulated domes supported by substructure, six single-layer reticulated domes with different rise-span ratios and different substructures were designed. Then, the dynamic characteristics of the reticulated domes supported by substructure are analyzed. After that, incremental dynamic analyses were carried out for reticulated domes supported by substructure on multiple three-dimensional ground motion records. Based on incremental dynamic analysis data, eighteen ground motion parameters are analyzed and evaluated in terms of correlation, efficiency, and sufficiency. Based on characteristic responses at failure state of a large number of arithmetic cases, the seismic damage model of single-layer reticulated domes supported by substructure was established. The results show that the presence or absence of the substructure has a greater influence on the structural fundamental frequency, and the structural fundamental frequency decreases as the stiffness of the substructure decreases. The difference between the fundamental frequency of the structure without support column and the structure with 10-meter support column is as high as 24%. The acceleration spectrum intensity and PGA are more strongly correlated to the seismic responses of reticulated domes supported by substructure，and the efficiency and sufficiency are better than other ground motion parameters, which can be used as ground motion parameters for fragility analysis of schwedler single-layer reticulated domes supported by substructure. At the same time, when the height of substructure is the same, the seismic performance of the reticulated dome structure with small rise-span ratio is better, and the critical load due to the collapse of the structure is greater. The influence of the support height on the seismic performance of reticulated domes is not linear. Therefore, the height of the substructure should be selected reasonably when designing the structure.