A numerical code that simulates combustion phenomena occurring in a solid rocket motor is developed in this study using a preconditioning algorithm. A quasi-steady-combustion process was analyzed for a composite material in a submerged nozzle. The governing equations were solved using a dual-time stepping method combined with a finite volume method. The mass flux and pressure in the cell face were evaluated using the advective upwind splitting method scheme. The turbulence model uses a two-equation model combined with a turbulence closure model. The geometric conservation law is used to simulate transient propellant surface regression. The numerical results for solid rocket combustion were compared with experimental results with a composite propellant. The calculated pressure variation in the combustion chamber is in good agreement with the measured results.