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This paper considers a model of a Čerenkov laser consisting of a relativistic electron beam and a parallel plate waveguide loaded with a dielectric thin film. By units of numerical analysis, the improvement of the growth characteristics for the electromagnetic wave and the efficiency in energy conversion is discussed. In the Čerenkov laser, the growth of the electromagnetic wave is caused by the transfer of the kinetic energy of the electron beam to the electromagnetic energy. As a result, the drift velocity of the electron beam is decreased gradually so that the synchronism with the phase velocity of the electromagnetic wave cannot be maintained and an efficient transfer of energy is prevented. Thus, the permittivity of the dielectric material composing the waveguide is increased gradually along the direction of the propagation for the electromagnetic wave to reduce the phase velocity of the electromagnetic wave. In this manner, the synchronism with the drift velocity of the electron beam is maintained, leading to an efficient transfer of energy. The variation of the permittivity causes power loss due to the mode scattering of the electromagnetic wave or the reflection or conversion to higher-order uses. In this paper, the effect of the mode scattering is taken into account for detailed numerical analysis of the amplification characteristics for the electromagnetic wave. It is shown that the efficiency in energy conversion from the electron beam to the electromagnetic wave and the amplification characteristics of the electromagnetic wave can be significantly improved. [ABSTRACT FROM AUTHOR]