A consistent seismic hazard and fragility framework considering combined capacity-demand uncertainties is proposed, in light of the probability density evolution method (PDEM). The PDEM has solid theoretical basis in the reliability field, and it is integrated within the performance-based earthquake engineering (PBEE) for hazard-fragility assessment in this paper. During the analysis, the sample sets with different assigned probability are required to determine in advance, and the equivalent extreme events with virtual stochastic process are required to establish for solution. Both the uncertainties of capacity and demand are considered, and a combined performance index (CPI) is defined as concerned physical variable in PDEM, through pushover static and timehistory dynamic analyses. A non-stationary stochastic earthquake model is introduced using spectral representation of random functions, and the real characteristics of ground motions are reflected by one or two variables for each probability space. The peak ground acceleration (PGA) and spectral acceleration of the first period Sa(T1) of non-stationary stochastic ground motions are then obtained for each earthquake level, and the equivalent extreme events are also performed to discuss the statistical information of PGA or Sa(T1) through PDEM. The exceeding probability of PGA or Sa(T1) for each earthquake level is acquired, and a connection between the fragility value and hazard extent is built. The final 3D consistent hazard-fragility curves are then given, and the exceeding probability for different limit states, earthquake levels as well as intensity exceeding conditions can be predicted. Moreover, a comparison with the four classic approaches in the state-of-the-art is performed to verify the accuracy of PDEM procedure. In general, the framework avoids the pre-defined lognormal fragility shape and proves the combined efficiency and accuracy with the Monte Carlo simulation (MCS). The consistency from probabilistic hazard to fragility is realized without re-selecting earthquake waves, which is mainly attributed to the application of PDEM and non-stationary ground motions. The proposed framework provides new ideas for the consistent non-parametric hazard and fragility assessment scheme in the PBEE. •Propose a consistent seismic hazard-fragility framework based on the PDEM and non-stationary stochastic earthquake.•Consider the combined capacity-demand uncertainties and a combined performance index with different assigned probability.•Give the 3D hazard-fragility curves incorporating different limit states, earthquake levels and intensity exceeding conditions.•Avoid the predefined lognormal curve shape and prove the combined efficiency and accuracy.