A lossy ceramic-loaded waveguide is positive to promote the stability and performance of the gyrotron traveling-wave amplifier (gyro-TWT). In this paper we develop the electron cyclotron maser linear theory on the basis of the field expressions in the lossy ceramic-loaded waveguide. By systematic numerical calculation, we find that both the field patterns and the dispersion curves have one-to-one mapping relation between the modes in ceramic-loaded waveguide and that in empty cylindrical waveguide. With the Laplace transform, the linear theory could calculate the field profile and the threshold of an absolute instability oscillation. The linear theory is also used to study the influence of the magnetic, current and ceramic layer on the amplification characteristics. These results are promotive to the application of the lossy ceramic in a gyro-TWT and the development of the high stable gyro-TWT.