Numerical simulation of 3D rough surfaces based on Fast Fourier Transform (FFT) is revisited. A more systematic approach, which is an extension of the current FFT based simulation models, is proposed to approach surface reconstruction. Moreover, the simulation of the surfaces with machining signature by prescribing the parameters, take ultrasonic-assisted grinding as example, has been taken as the research focus for the first time.The effectiveness is tested by three cases of simulation examples. Excepting the surface with exponential autocorrelation function, the simulation of surfaces with grinding machining marks is considered both by prescribing the theory autocorrelation function and by measuring a small area as a sample. The results show that the proposed method has great potential in engineering application.