A numerical method to perform large-eddy simulations (LES) of nonpremixed liquid oxygen/methane (LOx/CH4) combustion at supercritical pressures is presented and the computational results are compared with available experimental data. The injection conditions of the considered test case resemble those in typical liquid-propellant rocket engines (LRE). Thermodynamic nonidealities are modeled using the Peng–Robinson (PR) equation of state (EoS) in conjunction with a novel volume-translation method to correct deficiencies in the transcritical regime. The resulting formulation is more accurate than the standard cubic EoS's without deteriorating their good computational efficiency. The real-gas thermodynamics model is coupled with the steady laminar flamelet model (SLFM) for turbulent nonpremixed combustion to incorporate chemical reactions at reasonable computational cost in the LES. A reduced reaction mechanism, which is validated with respect to the full mechanism, is used to generate a flamelet library. A comparison of the LES result with available OH* measurements shows that important flow features are well predicted.