The low-temperature behavior of proteins under high pressure is not as extensively investigated as that at ambient pressure. In this paper, we study the dynamics of a hydrated protein under moderately high pressures at low temperatures using the quasielastic neutron scattering method. We show that when applying pressure to the protein-water system, the dynamics of the protein hydration water does not slow down but becomes faster instead. The degree of "softness" of the protein, which is intimately related to the enzymatic activity of the protein, shows the same trend as its hydration water as a function of temperature at different pressures. These two results taken together suggest that at lower temperatures, the protein remains soft and active under pressure.