Unsteady burning of n-pentane liquid droplet quiescent in high-pressure oxidizing air is investigated with emphasis placed on rigorous calculation of droplet vaporization. Fully coupled conservation equations in conjunction with global reaction kinetics for chemistry are preconditioned and time-integrated by means of a dual time-stepping technique with pertinent boundary conditions. Properties of equilibrated vapor-liquid interface are evaluated by the method of Soave-Redlich-Kwong equation of state along with consistent set of mixing rules for multi-component mixtures. Envelope flame propagates persistently with gradually increasing peak flame temperature as long as droplet remains in liquid phase. At all pressures, ignition is immediate and resultant steep temperature gradient at interfacial boundary aids in the activation of vaporization, but its extent decreases at later times as the droplet surface temperature arrives at its pseudo wet-bulb value. Ignition is immediate with continuous initial temperature distribution in the vicinity of interfacial boundary and renders an impulsive rise in droplet surface temperature. Other representative pressure effects on evolving droplet combustion are also presented and discussed.