We develop an AFM simulation program in non-contact mode, that uses the feedback process in which the cantilever moves up and down by comparing the amplitude with the initial steady-state amplitude. It can measure the shape of any given sample in 1/100 or 1/1000 nm scale. Since the initial position of AFM tip and bimorph amplitude are key factors in the non-contact mode simulation, we determine the appropriate initial conditions by considering the two major principles. First, the tip and the surface must not contact in the process of simulation. Second, tip``s motion must be affected by the interaction force between the tip and the sample. Not only the numerical solution but the analytic solution obtained by the discrete Fourier transform (DFT) are used in the simulation.