The purpose of this work is to investigate the effects of adding hydrogen to the fuel on the combustion induced vortex breakdown flashback phenomenon in a combustion chamber. An atmospheric research burner is selected for studies and the analysis is performed using numerical simulations. In order to model the turbulence-chemistry interactions, the EDC combustion model is utilized and the GRI 2.11 reaction mechanism is used to investigate the combustion process as carefully as possible. The present studies are performed keeping the exit temperature constant. To do this, by adding any amount of hydrogen to the premixed inlet flow, the methane is decreased by using the trial-and-error until the mass averaged exit temperature remains almost constant. The purpose of applying this limitation is to keep the cycle operational condition unchanged that is important for adding hydrogen to the existing combustion chambers especially from technological viewpoint. In addition, the thermal NOx production is controlled. In the following, the effect of hydrogen addition on the flame thickness and flame shape is investigated and finally, the effect of operating pressure on the flashback behavior is analyzed.