FeRh has been extensively studied because of metamagnetic phase transitions between the antiferromagnetic (AFM) and the ferromagnetic (FM) phase observed in this material. In this work, Brillouin light scattering (BLS) is used to detect magnons in metamagnetic FeRh. Appearance and disappearance of magnon scattering peaks with variation of temperature illustrate the transformation of FeRh into the FM and AFM phases, respectively. The dependence of frequency on temperature indicates significant change thus characterizing metamagnetic phase transitions in FeRh, since the temperature dependence of the magnon frequency shift mainly follows the saturation magnetization temperature dependence. In addition, a considerable increase of full width at half maximum (FWHM) linewidth of Stokes peak for FeRh is explained by the enhancement of magnetic damping. It is further found that the Dzyaloshinskii–Moriya interaction (DMI) takes place in single-layer FeRh with the DMI energy D affected by the first-order phase transitions in FeRh. These results provide an insight into the magnon dynamics in metamagnetic materials as well as offer new ways toward a modulation of magnetic damping in a wide range, which will be useful in the design of multifunctional spintronic devices.