Numerical modeling of near-critical mixing and combustion processes is a quite challenging task, due to the non-ideal thermodynamic effects and the abrupt variation of the transport properties. In the supercritical conditions, the surface tension and the vaporization heat approach zero, and the isothermal compressibility and the specific heat increase significantly. Compared to the subcritical propellant mixture properties, the propellant mixtures in the supercritical environment have the distinctly different characteristics such as liquid-like density and gas-like diffusivity. This study has been mainly motivated to numerically model the mixing and reacting flow processes encountered in the liquid propellant rocket engines. To account for the non-ideal thermodynamic effects, the propellant mixture properties are calculated by using SRK equation of state model In order to realistically represent the turbulence-chemistry interaction in the turbulent nonpremixed flames encountered in the supercritical real-fluid propellant combustion processes, the flamelet approach based on the real-fluid flamelet library has been adopted. The present real-fluid flamelet model has been applied to numerically investigate the gaseous hydrogen/cryogen liquid oxygen coaxial jet flame at the supercritical pressure. Based on numerical results, the detailed discussions are made for the real-fluid effects and the precise structure of the transcritical gaseous hydrogen/ liquid oxygen coaxial jet flame.