The present study numerically simulates self-excited instabilities of hydrogen-blended natural gas flames in a lean premixed gas turbine combustor with variable chamber length. In order to effectively predict the thermoacoustic instability within the detailed geometry of the combustor, the Helmholtz equation is discretized with a Galerkin finite element method on a three-dimensional hybrid unstructured mesh. The unsteady heat release rate is modeled with an experimentally measured flame transfer function. The non linearity associated with the flame response term is handled with an iterative method, and the large-scale eigenvalue problem is solved by means of the shift-invert method of the ARPACK (ARnoldi PACKage) software. The present Helmholtz solver reproduces the experimentally observed instabilities in terms of the mode frequency and the chamber length range of self-excited pressure oscillations which are significantly affected by the hydrogen enrichment of natural gas fuel. The effects of the acoustic boundary condition and the flame response model on the predictive accuracy are also discussed. (C) 2017 Elsevier Ltd. All rights reserved.