The sound velocities of water in the Hugoniot states are investigated by laser shock compression of precompressed water in a diamond anvil cell. The obtained sound velocities in the off-Hugoniot region of liquid water at precompressed conditions are used to test the predictions of quantum molecular dynamics (QMD) simulations and the SESAME equation-of-state (EOS) library. It is found that the prediction of QMD simulations agrees with the experimental data while the prediction of SESAME EOS library underestimates the sound velocities probably due to its improper accounting for the ionization processes.