Given unsteady operating conditions, the combustion process in gas turbine combustor often suffers from equivalence ratio fluctuations (ERFs), which induce combustion instability. In this study, the effects of ERFs on a swirl-stabilized premixed flame were studied by large eddy simulation (LES). A new combustion model with turbulence modification and a two-step methane oxidation mechanism were employed to simulate the interaction between turbulence and chemical reactions. In this study, LES was first validated by comparing the simulation results with the corresponding experimental data of a baseline case. Furthermore, two types of ERFs with different frequencies (40 and 160 Hz) were set on the inlet surface of the combustor, and flame responses were predicted by LES. With fluctuation frequencies of 40 and 160 Hz, the inner shear layer was strengthened, and evident corresponding vortices were generated. Furthermore, a more conspicuous variation was observed at 40 Hz, and it meant that a stronger combustion instability was induced by ERFs with a lower frequency.