A record based approach has been developed for the simulation of spatially correlated ground motion. This procedure uses autoregressive model to establish a power spectrum, and uses the multivariate linear prediction to simulate the parameter of unknown position. The random factor of earthquake is relected by Gaussian distribution random number, and the known records are subdivided into a sequence of time windows to account for its temporal variation. Compare of the simulated record and the true record show that this procedure is accurate and reasonable, and it is applicable for the design of discretely supported systems.