The tapping-mode atomic force microscope (TM-AFM) is a very useful tool to investigate the morphology and the physical properties of sample surface. The tip-sample contact process and phase contrast of TM-AFM is studied by numerical simulation. The cantilever-tip ensemble is simply modeled as a damped harmonic oscillator driven by an actuator. The effects of tip-sample distance zc and the Young modulus of sample Es on the contact time between the tip and sample tc, the deformation of the sample surface Dz and the contrast of phase image have been investigated. The results show that both tc and Dz decrease with increasing Es or zc. A little amount of energy dissipation can occur when the tip is tapping on the sample. Moreover, when zc is fixed, the phase shift of the sample with large Es is found more remarkable than that with small Es. The experimental observation of phase image performed on Au film dispersed with Au clusters supports the simulation results.