The present study proposes two sets of correlations of heat transfer to supercritical water for the cases with given heat flux and given wall surface temperature, respectively. Three steps are taken to develop the new correlations. At first a large data base was established. The reliability of each test point in the data base was assessed with respect to its consistence and reproducibility. In the second step, important dimensionless parameters were identified with two different approaches, i.e. the Spearman's rank correlation and the group-wise statistic assessment. Both approaches led to the similar outcomes and identified the most important dimensionless parameters, which can be used to predict the heat transfer coefficient. In the third step, two sets of correlations were proposed for the cases of given heat flux and given wall surface temperature, respectively, to avoid iterative procedure and subsequently possible multiple solutions. Both correlations give reasonable prediction of the experimental data. Nevertheless, the correlation for the cases with given wall surface temperature shows much better accuracy than that for the cases of given heat flux.