In this paper, the interface phonons in a core-shell quantum dot are theoretically studied by a resonant Raman scattering (RRS) process. Fröhlich electron–phonon interaction is considered in the framework of the dielectric continuum approach. The Raman peaks are found to be sensitive to the size of strongly confined shell. The shift of the Raman resonant peaks is a consequence of the change of observed dispersion of the phonon frequency. The Raman intensity changes in the system with shell thickness, originating from the competition between the spacial distribution of electron wave function and the number of phonons joining in the RRS process. The analysis of the Raman spectra gives a physical explanation to the size-selective nature of the Raman process and some experimental results.