Active plasmonic band-stop filters based on single- and double-layer doped graphene metamaterials at the THz wavelengths are proposed and investigated numerically by using the finite-difference time-domain (FDTD) method. The metamaterial unit cell structure is composed of two parallel graphene nanoscale ribbons. Simulated results exhibit that significant resonance wavelength shifts can be achieved with a slight variation of the doping concentration of the graphene ribbons. Besides, the asymmetry double-layer graphene metamaterial device has two apparent filter dips while the symmetry single-, double-layer and asymmetry single-layer graphene metamaterial devices just only one. The metamaterials with symmetry single-layer and asymmetry double-layer graphene can be used as a high-sensitivity refractive sensor with the sensitivity up to 5100 nm/RIU and a two-circuit switch, respectively. These prospects pave the way towards ultrafast active graphene-based plasmonic devices for THz applications.