Protein dynamics is strongly influenced by the surrounding environment and physiological conditions. Here we employ broadband megahertz-to-terahertz spectroscopy to explore the dynamics of water and myoglobin protein on an extended time scale from femto- to nanosecond. The dielectric spectra reveal several relaxations corresponding to the orientational polarization mechanism, including the dynamics of loosely bound, tightly bound, and bulk water, as well as collective vibrational modes of protein in an aqueous environment. The dynamics of loosely bound and bulk water follow non-Arrhenius behavior; however, the dynamics of water molecules in the tightly bound layer obeys the Arrhenius-type relation. Combining molecular simulations and effective-medium approximation, we have determined the number of water molecules in the tightly bound hydration layer and studied the dynamics of protein as a function of temperature. The results provide the important impact of water on the biochemical functions of proteins.