In order to study the collapse process and failure behavior of space grid structure under earthquake action, and reveal the collapse mechanism of the structure, based on the incremental dynamic analysis method (IDA), the single-layer spherical reticulated shell structure is taken as the research object, and the cumulative effect of material damage is considered. The collapse process of the simulated reticulated shell structure under earthquake action is analyzed, and the influences of parameters such as cross-section size, span-to-span ratio, initial geometric imperfections, and number of bearing constraints on the collapse resistance of the structure are analyzed. The results show that under the action of strong earthquakes, considering the dynamic ultimate bearing capacity of the reticulated shell structure after damage, the ultimate bearing capacity of the reticulated shell structure is reduced by about 20%, and the proportion of plastic elements is increased by about 10%. When other parameters are constant, the reinforcing rods are strengthened. The reduction of the section and the span ratio can improve the dynamic ultimate bearing capacity of the reticulated shell. The reticulated shell is very sensitive to the initial geometrical defects. When the defect is 1/100 of the span, its ultimate bearing capacity is reduced by about 30% compared with the complete structure. After the bearing restraint is halved, the cumulative effect of the damage reduces the seismic bearing capacity of the structure by about 10%. Therefore, at the beginning of structural design, the effects of cumulative effects of material damage should be considered.