Supercritical water-cooled reactor (SCWR), one of six conceptual designs of the next-generation advanced nuclear system, is known as its high thermal efficiency and simplified plant systems because of the special thermophysical properties of supercritical water. Computational fluid dynamics (CFD) has been applied in the studies of supercritical water to provide a better understanding of the heat transfer mechanisms. In this study, the influences of turbulence models (standard k-ε, realizable k-ε, and RNG k-ε model using the enhanced wall function, and standard k-ω and SST k-ω models using the low-Re model) on flow and heat transfer of supercritical water in circular channel were discussed. Meanwhile, the effects of various near-wall Y-plus on the calculated result were compared with Yamagata experimental data. The results of SST k-ω model showed better agreement than other models with the relative error less than 1%. The computed wall temperature for various near-wall mesh sizes showed that Y-plus values should preferably be equal to or smaller than 1. At the same time, the radial distribution of velocity, density and temperature was analyzed at the three sections (before the pseudo-critical temperature, around the pseudo-critical temperature, and after the pseudo-critical temperature). This work can provide information for choosing turbulence model when analyzing supercritical water by numerical simulation.