Graphene shows the advantages of high carrier mobility,flexible tunability without varying physical geometrical parameters,and strong mode confinement,which is a good complementary material for the exploration of surface plasmons(SPs)and MMs devices.Based on the graphene pattern structures,the tunable transmission properties of the metamaterials(MMs)has been investigated in the terahertz and near-IR spectral regimes,including the influences of graphene Fermi level,structural parameters and different kinds of substrate materials.The results manifest that in the THz regime the intra-band contribution dominates,and the transmission spectral curves can be modulated in a wide range with the changes of the Fermi level.For instance,the frequency modulation depth can reach more than 50%,and the amplitude modulation depth is about 80%on condition that the Fermi level changes in the range of 0.1-1.0 eV.While in the near-IR spectral range,the larger energy of incident light,the inter-band contribution plays an important role.As Fermi level increases,the inter-band contribution decreases,resulting into the graphene permittivity and resonant curves modulates significantly.Compared with original MMs devices,the complementary structure shows much shaper response curves,which can be used to fabricate filters and switchers.In addition,by depositing the graphene circular patterns on the substrate with larger dielectric substrate,the transmission dip displays obvious red-shift.The results are very helpful to design graphene based tunable waveguides device in the future.