In this paper, few-layer porous graphene is integrated onto the surface of a metasurface layer to provide a uniform static electric field to efficiently control liquid crystal, thereby enabling flexible metamaterial designs. We demonstrate a tunable cross-shaped metamaterial absorber with different arm lengths driven by this combined metasurface and graphene electrode. The resulting absorber supports a resonant frequency tunable from 0.75 to 1 THz with a high-quality factor, and amplitude modulation of ~80% at these frequencies with an applied voltage of 10 V. Furthermore, the near-field intensity and hot spot distribution can be manipulated over a broad range.