Abstract: Due to the randomness and the spatial variability of ground motion, the nonlinear behavior of isolation bearings and the limited number of isolation bearings installed in each bridge, the seismic response analysis of an isolated bridges is a typical multi-input locally nonlinear random vibration problem. The Bouc-Wen model is used to describe the nonlinear restoring force of isolation bearings, and then the nonlinear equation of motion of isolated bridges under multi-support seismic excitation is established. The nonlinear equation of motion is rewritten as a quasi-linear equation expressed in terms of state variables. Based on the precise time-integration method and the Range-Kutta method, an explicit time-domain dimension-reduced iteration scheme is established. Using this efficient scheme, the statistical characteristics of the random seismic responses of isolated bridges under multi-support seismic excitation are calculated by stochastic simulation. Numerical examples show the efficiency of the proposed approach and its application in the nonlinear random vibration analysis of isolated bridges under multi-support seismic excitation.