Turbulent convection heat transfer of fluids at supercritical pressures can experience abnormal heat transfer phenomena as the fluid temperature approaches the pseudo-critical temperature. A better understanding of these abnormal heat transfer characteristics is essential to develop ways to assure the security and reliability of engineering designs. In this study, we analyze the turbulent convection heat transfer characteristics of supercritical pressure fluid flow in a vertical heated tube using the field synergy principle. A turbulent Prandtl number model that is a function of the flow conditions as well as the physical properties is used in a low Reynolds number turbulence model with validations against experimental data. The validity of the field synergy principle is extended here to analyze convection heat transfer of supercritical pressure fluids where the heat transfer rate is a function of the synergy between the velocity and temperature gradients. Numerical simulation results show that when heat transfer deterioration occurs, the synergy angle between the velocity and temperature gradient vectors increase. The field synergy number could be used as an indicator to quantitatively identify the degree of heat transfer deterioration. The results presented here provide a basis for further research on enhancing turbulent convection of supercritical pressure fluid.