The combustion light gas gun (CLGG) uses a low molecular weight gas as the propellant to burn, expand and propel the projectile out of the barrel with higher muzzle velocities. In order to better understand the interior ballistic process of CLGG, an multidimensional combustion and flow model for CLGG is established. It contains unsteady Reynolds-averaged Navier-Stokes (RANS) equations, the RNG k-ε two equation turbulence models, and the Eddy-Dissipation Model (EDM) of combustion. Simulation of the interior ballistic process of CLGG is carried out with a propellant of hydrogen and oxygen mixture charged at a particular initial condition. Results show that the spherical front flames spread from the ignition points which divide the flow field as burned and unburned regions in the initial period and expand to the whole flow field subsequently. The filling error of propellants in the chamber will affect the interior ballistic performance, but the impact is relatively small.