Gate-controllable transmission of terahertz (THz) radiation makes graphene a promising material for making high-speed THz wave modulators. However, to date, graphene-based THz modulators have exhibited only small on/off ratios due to small THz absorption in single-layer graphene. Here we demonstrate a ∼50% amplitude modulation of THz waves with gated single-layer graphene by the use of extraordinary transmission through metallic ring apertures placed right above the graphene layer. The extraordinary transmission induced ∼7 times near-filed enhancement of THz absorption in graphene. These results promise complementary metal-oxide-semiconductor compatible THz modulators with tailored operation frequencies, large on/off ratios, and high speeds, ideal for applications in THz communications, imaging, and sensing.