The values of the nonlinear refractive index coefficient for various materials in the terahertz frequency range exceed the ones in both visible and NIR ranges by several orders of magnitude. This allows to create nonlinear switches, modulators, systems requiring lower control energies in the terahertz frequency range. We report the direct measurement of the nonlinear refractive index coefficient of liquid water by using the Z-scan method with broadband pulsed THz beam. Our experimental result shows that nonlinear refractive index coefficient in water is positive and can be as large as 7×10-10 cm2/W in the THz frequency range, which exceeds the values for the visible and NIR ranges by 6 orders of magnitude. To estimate n2, we use the theoretical model that takes into account ionic vibrational contribution to the third-order susceptibility. We show that the origins of the nonlinearity observed are the anharmonicity of molecular vibrations.