We present a simple model which estimates the influence of quantum effects from molecular vibrations on the equation of state of water under high pressures and temperatures. This model is combined with an ab initio equation of state of water generated by quantum molecular dynamics (QMD) simulations employing density functional theory for the electrons and a classical algorithm for the ions. We calculate the specific heat capacity as well as the principal Hugoniot curve, especially the Hugoniot temperature, in accordance with experiments.