Ammonia–methane (NH3–CH4) mixtures have potentials to serve as low-carbon fuels for gas turbines. Recent studies demonstrated that secondary air injection was an effective strategy to reduce NOx emissions from the combustion of NH3–CH4–air mixtures. However, the effects of secondary air injection on the performance of thermoacoustic instability of NH3–CH4–air flames remain unknown. To this end, this study experimentally investigated the thermoacoustic instability performance of a premixed, swirl-stabilized NH3–CH4–FF air combustor without and with secondary air injection. Without secondary air injection, thermoacoustic instabilities were widely detected at NH3 ratios below 50% (by volume). It was discovered that such instabilities were significantly suppressed by secondary air injection over a wider range of operating conditions. In conjunction with the analysis of the flame and flow dynamics, it was revealed that the secondary air injection suppressed the large amplitude axial oscillations of the flame and the flow field. Combined with the experimental results, it was inferred that the introduction of secondary air changed the velocity and pressure distribution downstream of the primary combustion zone, which in turn affected the formation and evolution of the vortex structures, thereby mitigating thermoacoustic coupling. Finally, emission measurements were discussed and the results indicated that the secondary air injection strategy reduced unburnt NH3 and CO emissions to a certain extent as well as decreased NOx emissions at specific equivalence ratios.