Metal-graphene photonic crystal-metal composite structures can achieve multi-band absorption. In order to understand the absorption characteristics of the composite structure, the influence of visible band structure parameters on multi-band absorption characteristics was studied with transfer matrix method. The results show that, central wavelength of each absorption band is independent of the chemical potential of graphene. The number of absorption bands is related to the number of periodic units of graphene photonic crystals and the optical thickness of dielectric layer. The larger the number of periodic elements, the greater the optical thickness of the dielectric layer, the more the number of absorption bands. The influence of the thickness of the two metal layers on the absorption characteristics is different. In order to make the optical absorption as high as possible, the metal layer on the side of the substrate should be as thick as possible. The thickness of the metal layer on the side of the incident space has an optimal value. When the parameters are selected reasonably at normal incidence, the absorption rate of each main absorption peak can be more than 90%. The results provide a reference for the development of multi-band optical absorbers based on graphene.