This paper presents a study of the influence of non-denaturing hydrostatic pressure on the relaxation dynamics of lysozyme in solution, which combines molecular dynamics simulations and quasielastic neutron scattering experiments. We compare results obtained at ambient pressure and at 3 kbar. Experiments have been performed at pD 4.6 and at a protein concentration of 60 mg/ml. For both pressures we checked the monodispersity of the protein solution by small angle neutron scattering. To interpret the simulation results and the experimental data, we adopt the fractional Ornstein–Uhlenbeck process as a model for the internal relaxation dynamics of the protein. On the experimental side, global protein motions are accounted for by the model of free translational diffusion, neglecting the much slower rotational diffusion. We find that the protein dynamics in the observed time window from about 1 to 100 ps is slowed down under pressure, while its fractal characteristics is preserved, and that the amplitudes of the motions are reduced by about 20%. The slowing down of the relaxation is reduced with increasing q-values, where more localized motions are seen.