The paper describes preliminary results of a molecular dynamics simulation study on the influence of non-denaturing hydrostatic pressure on the structure and the relaxation dynamics of lysozyme. The overall compression and the structural changes are in agreement with results from recent nuclear magnetic resonance experiments. We find that moderate hydrostatic pressure reduces essentially the amplitudes of the atomic motions, but does not change the characteristics of the slow internal dynamics. The latter is well described by a fractional Ornstein-Uhlenbeck process, concerning both single particle and collective motions.