Recently, oxy-combustion cycles with CO2 dilution have been of interest to eliminate NOx emission and to facilitate CO2 capture. Theoretically, they are operated in an overall stoichiometric condition. In addition, high pressure is preferred not only for better thermal efficiency but also for easier CO2 capture and storage. In this study, a triple-coaxial-tube was selected as the simplest conceptual design for an oxy-combustion burner at elevated pressure. Flame stabilization, soot emissions, and combustion efficiencies were investigated in relation to variation of the tube size, CO2 dilution ratio, and pressure. As a result, a jet Reynolds number and CO2 diffusion could explain the flame stabilization limits. Soot emission could be reduced at atmospheric pressure when the fuel-tube tip was moved into the middle oxidant tube, which also improved the combustion efficiency. Nevertheless, serious soot emissions recurred at excessive fuel flow rates and at elevated pressures. In such conditions, a lifted flame detached from the fuel-tube tip could be employed by increasing the flow rate or enhancing the CO2 dilution, and the soot emission was reduced again without losing combustion efficiency. Finally, the flame-stabilization mechanisms of the attached flame and of the lifted flame were discussed and optimized designs and operating conditions were proposed for less soot emission and better combustion efficiency at higher pressures.