There are two kinds of stochastic seismic ground motion simulation methods： frequency-domain methods and timedomain methods. Based on the time-domain model of single filtered white noise， this paper proposes the time-domain representa? tion for simulating stationary and non-stationary seismic ground motion processes. In essence， the time-domain representation can be regarded as linear superposition of deterministic functions modulated by a series of standard orthogonal random variables， and the set of orthogonal random variables is defined as the form of random orthogonal functions to achieve efficient dimension-reduc? tion. Therefore， by introducing three kinds of random orthogonal functions， i.e.， Legendre orthogonal polynomial of non-Gaussian type， Hartley orthogonal basis and Hartley orthogonal elementary of Gaussian type， the acceleration process of seismic ground mo? tion can be accurately represented in the time-domain model with only one elementary random variable. Numerical examples of seis? mic stationary ground motion process show the effectiveness of the proposed method， which is superior to the Monte Carlo meth? od. The analysis of fully nonstationary seismic ground motion shows the engineering applicability of the proposed method.