The numerical procedure for the burning of Ammonium Perchlorate (AP) with a Fuel-Binder (Hydroxyl Terminated Polybutadience HTPB) heterogeneous propellant is presented. This model accounts for the one-step reaction mechanism for the primary diffusion flame between the decomposition products of the Binder (B) and the oxidizer AP and allowed for the complete coupling between the gas-phase physics, the condensed-phase physics, and the unsteady non-uniform regression of the propellant surface. The parameters used in this model are fitted to experimental data for the combustion of AP/Binder. The propagation of the unsteady non-planer regression surface is described, using the Essentially-Non-Oscillatory (ENO) scheme with the aid of the level set strategy. The Alternating-Direction-Implicit (ADI) solver is employed to solve the full Navier-Stokes equations in the gas phase. The results show the effect of various parameters on the surface propagation speed, flame structure, and the burning surface geometry. A comparison between the computational and experimental results is presented.