The regulatory restrictions, currently acting, impose a significant reduction of the Greenhouse Gas (GHG) emissions. After the coal-to-gas transition of the last decades, the fossil fuel-to-renewables switching is the current perspective. However, the variability of energy production related to Renewable Energy Sources requires the fundamental contribution of thermal power plants in order to guaranty the grid stability. Moving toward a low-carbon society, the industry is looking at a reduction of high carbon content fuels, pointing to Natural Gas (NG) and more recently to hydrogen-NG mixtures. In this scenario, a preliminary study of the BERL swirled stabilized burner is carried out in order to understand the impact of blending natural gas with hydrogen on the flame morphology and CO emissions. Preliminary 3D CFD simulations have been run with the purpose to assess the best combination of combustion model (Non Premixed and Partially Premixed Falmelets), turbulence model (Realizable k ɛ and the Reynolds Stress equation model) and chemical kinetic mechanism (GriMech3.0, GriMech 1.2 and Frassoldati). The numerical results of the BERL burner fueled with natural gas have been compared with experimental data in terms of flow patterns, radial temperature profiles, O2, CO and CO2 concentrations. Finally, a 30% hydrogen in natural gas mixture has been considered, keeping fixed the thermal power output of the burner and the global equivalence ratio.