Excellent-performance terahertz (THz) modulators based on graphene/ionic liquid/graphene sandwich structures are demonstrated. The modulation covers a broadband frequency range from 0.1 to 2.5 THz with a modulation depth of up to 99% by applying a small gate voltage of 3 V. The outstanding performance of the proposed devices is due to the conical band structure of the graphene and the powerful gating effect of the ionic liquid in proximity to the graphene.