A Fourier expansion method is introduced to simulate the noncontact atomic force microscopy (NC-AFM) images in an efficient way, where three dimensional (3D) tip-surface interaction force distribution calculated by the first-principles density functional (LDA) calculations are fitted to an analytical function. As an example of application of this method, we adopt a Si(111)root 3 X root 3 R30 degrees-Ag surface. Force spectroscopies and 2D images for different tip height are presented.