A critically coupled resonator (CCR) is a thin-film structure that can absorb nearly all of the incident electromagnetic radiation, leading to null scattering. In order to effectively achieve and control the critical coupling (CC) phenomena, we replace the polymer absorbing layer by a graphene-based multi-film structure. FDFD (finite difference frequency domain) method is used to solve the Maxwell equation, and the graphene's surface conductivity is calculated by using the Kubo formula. Our results demonstrate that the CC phenomenon is realized at the near-infrared frequency and the frequency of absorption peak can be engineered by the Fermi energy of the graphene sheets. With increasing Fermi energy the absorption peak moves to the longer wavelength side. The effective permittivity of a multi-film structure has a strong dependence on the thickness of the dielectric and the layer number of the grapheme sheets in the multi-film structure. It is found that the central frequency of the absorption peak shifts towards longer wavelength side with increasing layer number of the graphene sheets M and the thickness of dielectric d1. Moreover, we also demonstrate that the absorption efficiency is affected by the electron-phonon relaxation time and the incident angle. It is clear that the central frequency of the absorption peak has a slight shift and the absorption is changed with the relaxing time and incident angle. The results offer the theoretical basis to the design of graphene-based critical coupling devices and optical detectors.