We report the results of the computer simulation of a collection of particles interacting via an anisotropic potential proposed by Luckhurst and Romano and modified by scaling with part of the anisotropic well depth formalism employed by Gay–Berne. Using the molecular dynamics technique for 256 particles in the NVE ensemble, the system is shown to exhibit a variety of mesophases, as the temperature is lowered, and these are provisionally identified as isotropic, discotic nematic, a highly ordered fluid phase with some columnar features and a crystal.