The plasmonic mode in graphene metamaterial provides a new approach to manipulate terahertz (THz) waves. Graphene-based split ring resonator (SRR) metamaterial is proposed with the capacity for modulating transmitted THz waves under normal and oblique incidence. Here, we theoretically demonstrate that the resonant strength of the dipolar mode can be significantly enhanced by enlarging the arm-width of the SRR and by stacking graphene layers. The principal mechanism of light–matter interaction in graphene metamaterial provides a dynamical modulation based on the controllable graphene Fermi level. This graphene-based design paves the way for a myriad of important THz applications, such as optical modulators, absorbers, polarizers, etc.