Combustion instability causes severe problems, Such as fatal damage to lean premixed gas turbine combustors and shortening the lifetime of the overall system. In this study,, to understand the instability phenomena, an experimental study and a numerical simulation were conducted in a dump combustor with respect to the modulation of the fuel flow, that is, the choked fuel flow and the unchoked fuel flow. The fluctuations of pressure and heat release were measured by a piezoelectric pressure sensor and high-speed intensified charge-coupled device (ICCD) camera, respectively. Various combustion modes occurred in accordance with the equivalence ratio and the fuel Supply conditions. In the low-frequency instability mode, alternative flame behaviors were observed and result from the large equivalence ratio modulation. It is found that, especially in an unchoked fuel flow condition, the modulation of the fuel flow rate affects the characteristics of flame behavior and pressure fluctuations in a lean premixed flame.