Compared to other two-dimensional (2D) crystals with single or binary elements, 2D ternary layered materials have unique physical properties for potential applications due to the stoichiometric variation and synergistic effect. Here, we report the first investigation of lattice dynamics and interactions between the exciton and lattice degrees of freedom in a 2D ternary semiconductor: indium-selenide-bromide (InSeBr). Via linear polarization resolved Raman scattering measurements, we uncover three Raman modes in few-layer InSeBr, including two A(1g) and one E-g modes. Moreover, through the combination of temperature-dependent Raman scattering experiments and theoretical calculations, we elucidate that few-layer InSeBr would harbor strong coupling between excitons and phonons. Our results may provide a firm basis for the development and engineering of potential optoelectronic devices based on 2D ternary semiconductors. Published under license by AIP Publishing.