Numerical modeling was performed to investigate the developing turbulent flow and heat transfer characteristics of water near the critical point in a curved pipe. The renormalization group κ-ε model was used to account for the turbulent flow and heat transfer in the curved pipe at a constant wall temperature with or without buoyancy force effect. A control volume finite element method was used to numerically solve the three-dimensional fully elliptic governing equations for the problem. Due to the great variations in physical properties of water near the critical point, the turbulent structure can be significantly altered compared with the pure forced convection in the curved pipe. This study explored the influence of the near-critical pressure and wall temperature on the development of fluid and heat transfer along the pipe.