In this work we investigate high-frequency thermoacoustic instabilities in a FLOX ® gas turbine burner by means of large-eddy simulation (LES). This burner is operated at eight bar pressure with a mixture of hydrogen and natural gas. Experimental data for the pressure oscillations in the combustion chamber are provided here to validate the simulations. The LES is conducted using a splitting scheme for solving the equations for compressible, reactive flows. To model the filtered chemical source terms in LES two different models (namely an assumed probability density function (APDF) model and a thickened flame (TF) model) are used. Time resolved computational data are analyzed using multi resolution proper orthogonal decomposition. It is found that mainly three longitudinal and one mixed transversal-longitudinal modes cause the high-frequency instabilities in the combustor. Computed frequencies of these modes agree excellently with measured frequencies. Amplitudes of the modes are best reproduced by the use of the TF model (the APDF model overestimates the strength of the mixed mode). Further analysis of the computational data obtained with the TF model reveals that the thermodynamic instabilities are caused by an interaction of heat release with hydrodynamic instabilities in the mixing section of the burner.