Ramjets exhibit undesirable combustion instabilities under certain operating conditions. In this paper, large-eddy simulation(LES) and premixed combustion model have been efficiently implemented to study combustion instabilities in ramjet combustors. The main objective is to predict dominant frequencies and various flow features of the combustors. Combustion instabilities in the ramjet dump combustor have been numerically simulated. Low-frequency, large-amplitude instabilities are observed, and instability frequencies and flame spread during various operating conditions are in good agreement with experimental observations. The results show large vortex structures dominate the flame propagation and vortex convection coupled unsteady heat release excites pressure oscillation in ramjet combustor.