A new seismic failure criterion is proposed for the Kiewit-8 (K8) dome subjected to earthquakes based on key structural parameters. Firstly, the K8 dome models were built in the finite-element package ANSYS after considering the key structural design parameters. Secondly, the incremental dynamic analysis was undertaken resulting in a typical structural damage index Ds. These were introduced to undertake the nonlinear dynamic response history analyses at each increased level of seismic records intensity and permitted the calculation of collapse loads of domes. Three hundred three-dimensional seismic records based on the main influential factors of ground motion were selected as input seismic waves. Thirdly, the lognormal distribution was selected to appraise collapse loads to gain the dynamic collapse fragility curves for domes after comparing three maximum likelihoods. Then, the lower bound collapse loads with 95% probability of non-exceedance changing with structural parameters were determined. Finally, relationships between lower bound collapse loads and five key structural parameters were separated out by using numerical matching methods, followed by a new seismic failure criterion for all the relationships including the five key structural parameters and a safety factor of 1.5. The new seismic failure criterion will contribute to the safe design and construction of these excellent space structures worldwide, particularly in the countries which are prone to earthquakes.