Numerical simulation is performed to study turbulent convective heat transfer to fluids near the critical point in the entrance region of a vertical tube. This modeling includes the effects of large thermodynamic and transport property variations of the fluid. The effect of proximity to the critical point is also considered as well as the buoyancy force in the vertical tube. Due to the property variation effects and buoyancy force in the tube, there is slow approach to fully developed conditions. The effects of large property variations are considered with a modified mixing length model including density fluctuation. Predictions from the mixing length model are in good agreement with experimental data from the literature and other analyses. The results show a little higher value in turbulent diffusivity than the standard mixing length model. The buoyancy force in the vertical tube depends on fluid temperature and pressure. The buoyancy force parameters increase as the pressure approaches critical pressure due to the steep density gradient with temperature which affects the characteristics of fluid flow and heat transfer in the developing region. The distributions of heat transfer coefficient and friction factor along the tube are quite different from those of the constant property case.