Lean-burn combustion using higher spark energy can enhance the combustion characteristics and emission performance. A laser is electrodeless with a high energy ignition source and can achieve multi-point ignition easily. This paper presents the computational fluid dynamics (CFD) modeling of combustion of methane-air and hydrogen-air mixture in a constant volume combustion chamber (CVCC) by using multi-point laser-induced spark ignition (LISI). The numerical simulation is carried out using ANSYS Fluent software and a standard turbulence model (k–$\epsilon$) is used. The pressure-time history and reaction progress was plotted for various equivalence ratios (ϕ). Numerical result shows that multi-point ignition can completely burn methane-air and hydrogen-air mixture in the range of 0.77 to 1.68 and 0.36 to 4.1, respectively. The maximum peak pressure (Pmax) and shortest combustion duration were observed at ϕ of 1.29 for the methane-air mixture and ϕ of 1.0 for the hydrogen-air mixture. The relative error between the numerical and the experimental results from the literature are within 10%. The faster reaction progress was observed for the hydrogen-air mixture compared to the methane-air mixture for all equivalence ratios. Finally, the validated numerical model was used to predict the CO, CO2 and NOx emission trends. For the methane-air mixture, CO emission increases as the equivalence ratio increases. However, the maximum CO2 emissions were observed at stoichiometric conditions. The highest NOx emissions were observed for the hydrogen-air mixture compared to the methane-air mixture at a stoichiometric equivalence ratio.