In recent years, achieving active control over the electromagnetically induced transparency (EIT) effect in metasurfaces has attracted grown interests. A novel modulation strategy was designed and fabricated based on a graphene-metal hybrid structure. An active EIT metasurface was realized in the terahertz (THz) regime by simultaneously applying optical pump and bias voltage, where the amplitude modulation depth at the transparency window frequency reached 73%. The simulation and theoretical analysis indicate that the inner physical mechanism lies in the shorting effect of the graphene to the metal resonant structure. The higher the conductivity of graphene is, the stronger the shorting effect is, and the weaker the resonance strength becomes. The proposed graphene-metal hybrid metasurface provides an alternative way towards designing compact active terahertz switching devices, and has potential in terahertz communication applications.