Combustion of liquid-fuelled combustion in a high-temperature vitiated-air stream was studied. The mathematical formulation comprise the application of Eulerian conservation equation to the gas phase and Lagrangian equation of droplet motion. The latter is coupled with a droplet-tracking technique (PSI-CELL Model) which regard the droplet phase as a source of mass, momentum, and energy to the gaseous phase. Reaction rate is determined by taking into account the Arrhenius reaction rate based on a single-step reaction mechanism. The calculated profiles show somewhat uncertainess at the upstream, but bases data for designing the combustor followed by 2-phase flow were obtained.