Recently, the graphene-based absorber captures much attention due to its bright potential. In this paper, a modeling study of graphene-based absorber is made for variable magnetostatic bias, i.e., the magnetic circular dichroism (MCD). A strong MCD signal about Delta A-0.94 is obtained in 7 T for a uniform graphene-based absorber. By periodically patterning subwavelength holes on the graphene, the structured absorber exhibits two obvious peaks induced by cavity resonance and localized resonance of meta-surface in 0 T, respectively. As the magnetic field increases, the absorption peaks show quite different electromagnetic response for the two kinds of circularly polarized lights. Two distinct MCDs signals of 0.711 at 2.02 THz and 0.91 at 2.49 THz in 7 T are observed. The results are well explained by a modified equivalent circuit model. (C) 2014 AIP Publishing LLC.