The stability of a turbulent diffusion flame temperature in an atmospheric gas-turbine combustor is investigated experimentally over a range of operating conditions to study the combined effect of hydrogen-enriched- methane (as fuel) and oxygen with carbon dioxide (oxy-fuel, as the oxidizer) on the combustion flame stability. These conditions included varying fuel and oxidizer mixture compositions, swirl angles, and equivalence ratios. The fuel (i.e. methane) is enriched with hydrogen (H2) in a ratio that ranged from zero to 50%; where the oxidizer (pure oxygen) is mixed with carbon dioxide (CO2) in a ratio that ranged from zero up to the value of flame blow-off. Different swirl vane angles corresponding to different swirl numbers were considered. The results indicated that stable regime (flame) is achieved close to stoichiometric conditions at high oxygen (O2) to CO2 ratio and high H2 (50%) enriched fuel; while the flame blow-off occurred at low O2 to CO2 ratios (20% or less). High-level flame stability with moderate flame length and temperature were observed at the highest swirl vane angle.