We performed THz and GHz dielectric relaxation spectroscopy to investigate the reorientational dynamics of water molecules in the hydration shell of amphiphilic hyper-branched poly-ethylenimine (HPEI). Four Debye equations were employed to describe four types of water in the hydration shell, including bulk-like water, under-coordinated water, slow water (water molecules hydrating the hydrophobic groups and water molecules accepting hydrogen bonds from the NH2 groups) and super slow water (water molecules donating hydrogen bonds to and accepting hydrogen bonds from NH groups). The time scales of undercoordinated and bulk-like water show a slight decline from 0.4 to 0.1 ps and from 8 to 2 ps, respectively. Because of hydrophilic amino groups, HPEI molecules exhibit a strong retardation effect, where the time scales of slow and super slow water increase with concentration from 17 to 39.9 ps and from 88 to 225 ps, respectively.