The diffusive dynamics of hydration water in lysozyme is studied by high-resolution incoherent quasielastic neutron scattering spectroscopy and molecular dynamics (MD) simulations in a temperature range of 290 K<T<380 K. The hydration level of the protein powder sample is kept at h=0.35 gram of water per gram of dry protein to provide monolayer of water coverage on the protein surfaces. Two lysozyme samples, the H(2)O hydrated and the D(2)O hydrated, are measured in the experiments. The difference spectra of the two are used to extract the diffusive dynamics of the hydration water. The self-diffusion constant D of the hydration water is obtained from the analyses of the low-Q spectra. The Arrhenius plot of the inverse diffusion constant [i.e., log(1/D) versus 1/T] shows a dynamic crossover from a super-Arrhenius behavior at low temperatures to an Arrhenius behavior at high temperatures bordered at T(D)=345+/-5 K. We also observe a pronounced increase in the migration distance d of the hydration water molecules above T(D). We present evidence from the neutron scattering experiment that this dynamic crossover temperature in the hydration water coincides with that of the reversible denaturation of lysozyme determined by specific heat measurements. We further performed MD simulations of hydrated lysozyme powder to offer a plausible reason for this coincidence of the crossover phenomenon with the reversible denaturation of the protein.