Based on particle-in-cell simulations, we propose to generate sub-nanosecond pulses of narrowband terahertz radiation with tens of MW power using unique properties of kiloampere relativistic (2 MeV) electron beams produced by linear induction accelerators. Due to small emittance of such beams, they can be focused into millimeter and sub-millimeter spots comparable in sizes with the wavelength of THz radiation. If such a beam is injected into a plasma, it becomes unstable against the two-stream instability and excites plasma oscillations that can be converted to electromagnetic waves at the plasma frequency and its harmonics. It is shown that several radiation mechanisms with high efficiency of power conversion (∼1%) come into play when the radial size of the beam–plasma system becomes comparable with the wavelength of the emitted waves.