Numerical analysis has been carried out to investigate laminar convective heat transfer in a tube for supercritical water near the thermodynamic critical point. Fluid flow and heat transfer are strongly coupled due to large variations of thermodynamic and transport properties such as density, specific heat, viscosity, and thermal conductivity near the critical point. Heat transfer characteristics in the developing region of the tube show transition behavior between liquid-like and gas-like phases with a peak in heat transfer coefficient distribution near the pseudocritical point. The peak of the heat transfer coefficient depends on pressure and wall heat flux rather than inlet temperature and Reynolds number, Results of the modeling provide convective heat transfer characteristics including velocity vectors, temperature, and the properties as well as the heat transfer coefficient. The effect of proximity to the critical point is considered and a heat transfer correlation is suggested for the peak of Nusselt number in the tube.