Thermo-acoustic characterization of gas turbine combustion systems is crucial for a successful development of new gas turbine engines to meet emission and efficiency targets. In this context, it becomes more and more necessary to predict the limit cycle amplitudes of thermo-acoustic induced combustion instabilities in order to figure out if they can be tolerated or if they are above the critical design limit and will cause damage to the engine. For the prediction of limit cycle amplitudes, the nonlinear flame response of the combustion system is needed, which is represented in this work by the flame describing function (FDF). In this article, the identification of the FDF from a large eddy simulation (LES) is validated. The test case used was a premixed atmospheric swirl flame, for which experimental data on the FDF were available. First a steady reacting LES solution was obtained and compared to experimental data. The simulation was then excited by superimposing a mono-frequency harmonic wave on the velocity inlet boundary condition. Both the frequency and amplitude of the acoustic wave were varied to obtain the FDF. The calculated FDF was in good agreement with experimental data. At a frequency of 115 Hz, the heat release rate of the flame was found to saturate for larger excitation amplitudes.