A method for enhancing the efficiency of energy transfer from a relativistic electron beam to an electromagnetic wave in a Cherenkov laser is proposed. In a two‐dimensional Cherenkov laser composed of a planar relativistic electron beam and a parallel plate waveguide loaded with a dielectric grating, either one of the grating parameters, or the slot width and the groove depth, is tapered or gradually decreased in accordance with the decrease in the drift velocity of the electron beam. The numerical simulation demonstrates that sufficient efficiency enhancement can be achieved by a tapered dielectric grating. ©1996 American Institute of Physics.