To improve the computational efficiency and accuracy of reliability-based fatigue life prediction for complex structure, a time-varying particle swarm optimization- (PSO-) based general regression neural network (GRNN) surrogate model (called as TV/PSO-GRNN) is developed. By integrating the proposed space-filling Latin hypercube sampling technique and PSO-GRNN regression function, the mathematical model of TV/PSO-GRNN is studied. The reliability-based fatigue life prediction framework is illustrated in respect of the TV/PSO-GRNN surrogate model. Moreover, the reliability-based fatigue life prediction of an aircraft turbine blisk under multiphysics interaction is performed to validate the TV/PSO-GRNN model. We obtain the distributional characteristics, reliability degree, and sensitivity degree of fatigue failure cycle, which are useful for the turbine blisk design. By comparing the direct simulation (FE/FV model), RSM, GRNN, PSO-GRNN, and TV/PSO-GRNN, we observe that the TV/PSO-GRNN surrogate model is promising to perform the reliability-based fatigue life prediction of the turbine blisk and enhance the computational efficiency while ensuring an acceptable computational accuracy. The efforts of this study offer a useful insight for the reliability-based design optimization of complex structure.