Burning behavior of a fuel droplat under microgravity field has been studied to explore the effects of the ambient pressure. Experiments were performed by using a high pressure combustion chamber and a drop tower. The fuels employed were n-heptane and n-octane. Experiments have showed that spherical flames were obtained for ambient pressures both below and above the critical pressure of fuel. As the ambient pressure is increased, the burning rate constant increases, reaches a maximum at the critical pressure, and then decreases. Numerical calculations for the droplet burning process were performed by using the quasi-steady evaporation theory considering general material properties. The characteristic pressure dependency of the burning rate constant can be essentially predicted.