The addition of salts into protein aqueous solutions causes changes in protein solubility and stability, whose ability is known to be ordered in the Hofmeister series. We investigated the effects of Hofmeister salts on the picosecond dynamics of water around a lysozyme molecule using terahertz time-domain spectroscopy. The change in the absorption coefficient for 200 mg mL(-1) lysozyme aqueous solution by the addition of salts was found to depend on the salts used, whereas that for pure water was almost independent of salts. From the difference in the salt concentration dependence for various salts, it has been found that chaotropic anions make the dynamics of water around the lysozyme molecule slower, whereas kosmotropic anions make the dynamics faster. The ability of an anion to slow down the water dynamics was found to have the following order: SCN(-) > Cl(-) > H2PO4(-) > NO3(-) ≈ SO4(2-). This result indicates that the effects of anions on the dynamics of water around the lysozyme molecule are the opposite of those for bulk water. This finding agrees with a prediction from a molecular model proposed by Collins [K. D. Collins, Methods, 2004, 34, 300]. The results presented here are compared with the results from preferential interaction studies and the results from sum frequency generation spectroscopy. These discussions have led to the conclusion that the picosecond dynamics of protein hydration water strongly contributes to protein stability, whereas electrostatic interactions between protein molecules contribute to protein solubility.