Terahertz (THz) radiation, which lies in the far-infrared region, is at the interface of electronics and photonics. Narrow-band THz radiation can be produced by free-electron lasers and fast diodes^,. Broadband THz radiation can be produced by thermal sources and, more recently, by table-top laser-driven sources^,, and by short electron bunches in accelerators, but so far only with low power. Here we report calculations and measurements that confirm the production of high-power broadband THz radiation from subpicosecond electron bunches in an accelerator. The average power is nearly 20 watts, several orders of magnitude higher than any existing source, which could enable various new applications. In particular, many materials have distinct absorptive and dispersive properties in this spectral range, so that THz imaging could reveal interesting features. For example, it would be possible to image the distribution of specific proteins or water in tissue, or buried metal layers in semiconductors^,; the present source would allow full-field, real-time capture of such images. High peak and average power THz sources are also critical in driving new nonlinear phenomena and for pump–probe studies of dynamical properties of materials^,.