Experimental investigations were conducted into the heat transfer characteristics of supercritical water in a downward flowing cooling tube surrounded by pool boiling for the passive cooling system of the Generation-IV Supercritical-Water-Cooled Reactor (SCWR). The experimental parameters cover the extreme high ranges of pressure (23–27 MPa), mass flux (600–1000 kg·m−2·s−1), bulk fluid temperature (150–500 °C), and inner heat flux (98–1143 kW·m−2). A new thermal amplification system was applied to measure the heat transfer coefficient near the pseudocritical region under various mass fluxes and pressures. A sharp jump in the wall temperature and maximum heat transfer coefficient was observed at the pseudocritical point, and the mass flux and pressure exhibited different influences below and above the pseudocritical point. Based on the experimental data, a new heat transfer correlation for predicting the Nu is proposed for the subject cooling scenario. The proposed heat transfer correlation includes the density ratio and requires only the fluid properties at the bulk temperature. The mean absolute and root-mean-square error of the proposed correlation were about 7.94% and 9.60%, respectively. The proposed correlation can serve as a reference in the design of the passive cooling system of the SCWR.