The results on heat transfer to supercritical water heated above the pseudocritical temperature or affected by mixed convection flowing upward and downward in vertical tubes of 6.28-mm and 9.50-mm inside diameter are presented. Supercritical water heat-transfer data were obtained at a pressure of 23.5 MPa, mass flux within the range from 250 to 2200 kg/(m2s), inlet temperature from 100 to 415°C and heat flux up to 3.2 MW/m2. Temperature regimes of the tubes cooled with supercritical water in a gaseous state (i.e., supercritical water at temperatures beyond the pseudocritical temperature) were stable and easily reproducible within a wide range of mass and heat fluxes. An analysis of the heat-transfer data for upward and downward flows enabled to determine a range of Gr/Re2 values corresponding to the maximum effect of free convection on the heat transfer. It was shown that: 1) the heat transfer coefficient at the downward flow of water can be higher by about 50% compared to that of the upward flow; and 2) the deteriorated heat-transfer regime is affected with the flow direction, i.e., at the same operating conditions, the deteriorated heat transfer may be delayed at the downward flow compared to that at the upward flow. These heat-transfer data are applicable as the reference dataset for future comparison with bundle data.