A graphene-based terahertz negative-conductivity metasurface based on two types of unit cell structures is investigated under the control of an external bias voltage. Electrical characterization is conducted and verification is performed using a finite-difference time-domain (FDTD) and an optical-pump terahertz (THz)-probe system in terms of simulation and transient response analysis. Owing to the metal-like properties of graphene, a strong interaction between the metasurface and monolayer graphene yields a short-circuit effect, which considerably weakens the intensity of the resonance mode under passive conditions. Under active conditions, graphene, as an active load, actively induces a negative-conductivity effect, which enhances the THz transmission and recovers the resonance intensity gradually because of the weakening of the short-circuit effect. The resulting resonance frequency shows a blue shift. This study provides a reference value for combining graphene exhibiting the terahertz bias-driven negative-conductivity effect with metasurfaces and its corresponding applications in the future.