Large eddy simulations (LES) of premixed hydrogen-enriched swirling flames were performed to investigate the flame topology and combustion instabilities with different hydrogen concentrations. A compressible LES approach is utilised to account for the self-excited combustion dynamics. A transported probability density function (pd f) approach is adopted to account for sub-grid scale (sgs) turbulence-chemistry interaction, and the solution to the joint sgs – pd f evolution equation of the scalars is obtained by the stochastic field method. The chemistry is represented using a reduced chemical reaction mechanism containing 15 reaction steps and 19 species. The results revealed that as the concentration of hydrogen increases, the flame is shortened in the injecting direction and more confined in the cross-sectional direction, which is consistent with experimental observations. The self-excited limit-cycle oscillations for all considered cases were successfully reproduced, with the predicted peak frequencies of the chamber pressure spectra in excellent agreement with the measured values. The feedback loop of the oscillations is successfully captured and analysed with the temporal evolution of axial velocity and heat release presented.