Using shock wave loading and real time optical transmission measurements, the transmission spectra of liquid water compressed between the quartz windows under pressures in a range of 1-1.6 GPa are obtained. A discontinuity of liquid water at nearly 0.9 GPa during the shock is observed. Combining the phase diagram of water with calculation results, it is suggested that the discontinuity of liquid water is due to a possible phase transition from low density water to high density water under the experimental conditions. The method can also be used to study other transparent molecular liquids in shock compression experiments.