The effect of the electron-phonon interaction on the degenerate four-wave mixing was investigated theoretically for electrons confined in a core-shell quantum dot.Under the framework of effective-mass approximation,the interactions of electrons with different phonon modes in the core-shell system,including the confined longitudinal optical and the interface optical phonon modes,were investigated.The degenerate four-wave mixing on a ZnS/CdSe core-shell quantum dot as a function of pump photon energy with different incident photon energy and under different sizes was calculated.The results reveal that the polaron effects are quite important especially around the peak value of the third-order susceptibility.The influence of electron-LO-phonon interaction on the degenerate four-wave mixing is bigger than the influence of electron-IO-phonon interaction.By increasing the size of the quantum dots,the peaks of χ(3)DFWM will shift to lower energy,and the intensities of the peaks will greatly increase.