The chemical charging and following electrochemical discharging through the formation and decomposition of graphite intercalation compounds with sulfuric acid were studied on three host materials with different textures, viz., natural graphite flakes, vapor-grown graphite fibers and mesophase-pitch-based graphite fibers. In the course of electrochemical discharging in sulfuric acid containing nitric acid as oxidant, a competition between the de-intercalation and re-intercalation of sulfuric acid into the graphite gallery was observed and, as a consequence, a strong effect of the texture of the host graphite on the discharging process. On the mesophase-pitch-based graphite fibers with radial arrangement of the graphite basal planes in the cross-section of the fibers, electrochemical discharging with rather steady state voltage in long period was possible.