By using molecular dynamics simulations, the pressure dependence of the diffusion coefficient in a binary Lennard-Jones glass was calculated. Four temperature regimes were observed. The apparent activation volume fell from high values in the hot liquid to a plateau value. Near to the critical temperature of the mode coupling theory, it rose steeply but - in the glassy state - small values were again found; similar to those in the liquid. The peak of the activation volume at the critical temperature was in agreement with the predictions of mode coupling theory.Pressure Dependence of Diffusion in Simple Glasses and Supercooled Liquids. H.R.Schober: Physical Review Letters, 2002, 88[14], 145901 (4pp)