The large-eddy simulation (LES) model previously developed for cold flow in an axisymmetric ramjet combustor is extended to include a model for premixed fuel combustion. The combustion model explicitly uses a subgrid-scale local turbulent flame speed in the governing equation. This model not only reduces the computational effort, when compared to a model with detailed finite-rate chemical kinetics, but also avoids the potential error in the amount of heat release causd by numerical diffusion. Both stable and unstable combustion are simulated with evidence of decaying and growing pressure oscillations, respectively. The observed flow features on unstable combustion. such as a propagating hooked flame and its phase relation with the pressure oscillation, agree with experimental observations. These simulations clearly establish that the LES model contains the essential physics of combustion instability in a ramjet. Although the simulations show general qualitative features of combustion instability, further research is required to take into consideration the important effects of subgrid-scale turbulence on combustion instability. Extensive simulations using the resulting LES model may then lead to a better understanding of the physical processes involved in combustion instability.