The metamaterial perfect absorber (MPA) is a new type of electromagnetic wave absorber first proposed by Landy. Compared with the traditional electromagnetic wave absorber, MPA has many advantages, including ultra-high absorption efficiency, ultra-thin, compact structure, easily tunable resonances, etc. so it is gradually applied to ultra-sensitive sensing, imaging, detection and other fields. Nowadays, the MPA research focuses on two areas. One area focuses on the absorption efficiency modulation and absorption wavelength tuning, and the other area is to broaden the absorption bandwidth and achieve high absorptions at different optical frequencies. Previously, the MPA absorption efficiency modulation or absorption wavelength tuning was realized by changing the device structure or the surrounding medium material. But these methods can increase the difficulty in processing and increase the device volume. In order to achieve the control of absorption wavelength and absorption efficiency without increasing the difficulty in processing or the device volume. We propose to use vanadium dioxide and graphene as the materials of MPA, which has high absorption efficiency in the infrared band. It is found that the absorption efficiency of MPA at 9.66 μm wavelength can reach 96% when the temperature of vanadium dioxide is 5 ℃ by using finite difference time domain (FDTD) method. However, when the vanadium dioxide temperature rises to 68 ℃, the absorption efficiency of MPA suddenly drops to 2.8%. The modulation depth of absorption efficiency can reach 97.08%. We propose that the MPA be able to control not only the absorption efficiency, but also the absorption wavelength. By changing the voltage of graphene, the chemical potential E_f of graphene can be controlled and the absorption wavelength of MPA can be tuned. When E_f increases from 0.1 eV to 3 eV, the absorption wavelength of MPA will be blue-shifted from 9.66 μm to 6.46 μm. The magnetic field distribution of MPA at the absorption wavelength shows that the MPA has a high absorption efficiency because of the Fabry-Pérot (FP) cavity resonance is formed in MPA. Therefore, the change of structure parameters of MPA will affect its absorption characteristics. It is found by the FDTD method that the absorption wavelength of MPA will be redshifted, when the radius, thickness, period and thickness of the nanocolumn array increase. This study can provide theoretical guidance for designing and preparing the controllable MPA, which has compact structure and low process difficulty merits.