It is proposed the short-wavelength high-gain Cherenkov oscillator driven by supercurrent. In this concept, thin superconductor film, carrying dc current, is situated within a slow-wave structure (dielectric superlattice in a waveguide). It is shown that an amplification of the electromagnetic wave is possible when the wave phase velocity is close to the characteristic diffusion velocity of the order parameter phase. The small-signal exponential gain coefficient is calculated. Estimates show the proposed scheme be promising source of coherent THz radiation.