Abstract The first measurements of the surface diffusion coefficients in columnar discotic liquid crystal thread and film by an optical absorption technique are presented. A comparison of the results with the diffusion in the bulk specimen helps to introduce the number of diffusion sites in the surface and in the bulk. We propose then a structure of point defects in the mesophase. An estimation of jump frequency is deduced. The dependence of the surface diffusion versus the temperature seems in agreement with the Arrhenius law.