To evaluate the seismic performance of single-layer spherical reticulated shell, the randomness and non-stationarity of seismic excitations need to be sufficiently taken into account. In conjunction with the probability density evolution method (PDEM), the probabilistic information of dynamic response and reliability can be readily obtained. First, the random function based spectral representation method is employed to model the fully non-stationary seismic ground motions, which meets the requirements of different fortifications. Moreover, the average response spectrum accords well with the target response spectrum. Then, the instantaneous probability density evolution process of the shell’s maximum displacement is investigated from the perspective of PDEM. Further, two indices, which characterize the failure of the shell structure, are selected from macro and micro levels, respectively. By introducing the idea of equivalent extreme-value event, one can obtain the extreme value distribution of response for seismic reliability analysis. Finally, through carrying out the parametric analyses, the effect of different parameters on the seismic reliability of the shell can be evaluated. Compared with the traditional methods, the proposed method can evaluate the seismic performance of single-layer spherical reticulated shells from the perspective of randomness, which is much more reasonable. Besides, the tradeoff of efficiency and accuracy can be also ensured.