In response to the current situation where the seismic reliability of seismic-isolated curved girder bridges cannot fully consider the randomness and multidimensionality of seismic motion， this paper systematically studies the seismic performance of seismic-isolated curved girder bridges under multi-dimensional random seismic action from thea perspective of full probability. A dual particle， six-degree-of-freedom model of a seismic-isolated curved girder bridge is established and its nonlinear motion equations are derived. By introducing a stochastic model of the engineering seismic acceleration power spectrum， the spectral representation seismic-isolated random function method is used to generate multidimensional non-stationary vibration time history samples that conform to the same set system. The seismic acceleration time history samples are used as the random excitation input for the seismic-isolated curved girder bridge. The fourth-order Runge-Kutta method is used to obtain the dynamic time history data of the seismic-isolated curved girder bridge structure， and the TVD difference scheme is used to solve its generalized probability density evolution equation to quantify the probability information of the structural dynamic response during earthquake duration. Then， an extreme value stochastic process is constructed to obtain the displacement extreme value distribution functions and system reliability of the lower structure and isolation layer of the seismic-isolated curved girder bridge. The results indicate that considering the multidimensionality of non-stationary random seismic excitation amplifies the dynamic response of seismic-isolated curved girder bridge structures. The probability density evolution method shows superior performance in solving strongly nonlinear structural systems such as seismic-isolated curved girder bridges. By adjusting the reasonable values of the bridge deck width and curvature radius of the seismic-isolated curved girder bridge， the seismic performance of the seismic-isolated curved girder bridge can be improved.