A waveguide periodically loaded with lossy dielectric rings and metal rings is able to effectively control the attenuation of each mode. The is important for suppressing the absolute instability and enhancing the performance of a millimeter-wave gyrotron traveling wave tube amplifier (gyro-TWT). The modal mapping between the periodic waveguide and the uniform waveguide was systematically studied for a periodic ceramic-loaded cylindrical waveguide applied in TE01 mode gyro-TWT at Ka-band. It was revealed that, with a proper dielectric thickness, a higher order mode in uniform dielectric-loaded waveguide can be mapped to a lower order mode in smooth waveguide and the field distributions of the inter-mapped modes in vacuum region bear good resemblance to each other. A mode in periodic system exhibits complex mode distribution. In a period, the field distributions of the mode in the dielectric section and the metal ring section are mapped to those in uniform dielectric-loaded waveguide and smooth waveguide, respectively. The understanding of the modal mapping between the periodic dielectric-loaded waveguide and smooth waveguide is the precondition for the analysis of the complex electron cyclotron interaction in such a periodic system, which brings helpful guidance for the simplification of the physical model.