We focus on investigating the dielectric behaviors and the low-frequency texture transitions in a cholesteric liquid crystal (CLC) doped with graphene nanoplatelets (GNPs) by means of dielectric spectroscopy and measurements of electro-optical responses. The experimental results indicate that incorporating GNPs at a content of 0.5 wt% into the CLC leads to significant suppression of ionic behaviors, as manifested by the reduction in ionic density, diffusivity, and relaxation frequency. In addition, the electro-optical properties of the GNP-doped CLC cell show the lowered operation voltage for the switching from the planar to focal conic state and the absence of the low-frequency focal-conic-to-uniform-lying-helix texture transition. Such results are attributable to the effects of GNPs as nuclei in the CLC medium, giving rise to the repression of the ionic and electrohydrodynamic effects.