Abstract: The basic definitions of stationary random process and the principles of using spectrum decomposing to simulate the stationary random process were given. The three important factors to be considered when simulating stationary random process with MATLAB including selection of signal source, simulating algorithm and corresponding parameters, and regulation caused by different definition of the power spectral density. The procedure of simulating stationary random processes with MATLAB was illustrated by two examples: air turbulence and aircraft carrier motion at sea. The tested simulation results indicate that stationary random process can be simulated very well with MATLAB.