Higher harmonics of tapping-mode atomic force microscope carries information about the mechanical properties of the sample on a nanometer scale. Unfortunately, the vibration amplitudes of traditional atomic force microscope (AFM) cantilever at higher harmonics are too small for practical AFM imaging. Ritz method demonstrates that specific cutout on the cantilever can realize internal resonance to enhance higher harmonics. In this paper, by COMSOL finite element simulation, the laws for fundamental frequency, second resonance frequency and their ratio each as a function of the size of the cutout and the position of the cutout on the cantilever are achieved. Using focused ion beam to hole the cantilever makes the second resonance frequency close to 6 times that of the fundamental frequency and also the 6th harmonic enhanced. Moreover, we obtain the image of the 6th harmonic on our home-made higher harmonic system.