Efficient and stable operation of Cerenkov devices relies on effective mode control, which means efficient generation of the operation mode and effective suppression of the competition modes. This paper explores the feasibility of suppressing asymmetric modes by loading a conductivity anisotropic material in Cerenkov devices. We theoretically study the dispersion characteristics of a slow-wave structure (SWS) loaded with a conductivity anisotropic material. The theoretical analyses indicate that asymmetric modes such as the HE11 mode have a low net temporal growth rate in a SWS coaxially loaded with the anisotropic material, of which the azimuthal conductivity is in the transition region from good to poor conductor. Accordingly, an anisotropic material with suitable azimuthal conductivity effectively suppresses asymmetric mode competition while maintaining the original characteristics of the symmetric TM modes. Furthermore, we numerically investigate the effectiveness of asymmetric mode suppression by anisotropic material loading using a 3D particle-in-cell CHIPIC code. A coaxially loaded conductivity anisotropic material effectively suppresses the asymmetric HE11 mode in a Ku-band Cerenkov device, and a pure quasi-TEM mode is obtained in the output waveguide. The output power of the generator is 2.9 GW, and the efficiency is 44%. This study provides a feasible method to eliminate asymmetric modes in Cerenkov devices, which may lead to a wide range of applications.