We have fabricated a centimeter-size single-layer graphene device with a gate electrode, which can modulate the transmission of terahertz and infrared waves. Using time-domain terahertz spectroscopy and Fourier-transform infrared spectroscopy in a wide frequency range (10–10 000 cm–1), we measured the dynamic conductivity change induced by electrical gating and thermal annealing. Both methods were able to effectively tune the Fermi energy, EF, which in turn modified the Drude-like intraband absorption in the terahertz as well as the “2EF onset” for interband absorption in the mid-infrared. These results not only provide fundamental insight into the electromagnetic response of Dirac fermions in graphene but also demonstrate the key functionalities of large-area graphene devices that are desired for components in terahertz and infrared optoelectronics.