This study has been mainly motivated to numerically investigate the transient flame response to pressure oscillations in the gaseous hydrogen - liquid oxygen flames at supercritical pressures. The present analysis is based on the real-fluid transient flamlet model and the flame field is acoustically perturbed only by the sinewave oscillations in the frequency range from 1,000 Hz to 5,000 Hz. Based on numerical results, the detailed discussions are made for the flame response characteristics and the transient flamelet response associated with the high-frequency combustion instability in the liquid propellant rocket engines.