The pinning effect is studied in a Gaussian quantum dot using the improved Wigner-Brillouin perturbation theory (IWBPT) in the presence of electron-phonon interaction. The electron ground state plus one phonon state is degenerate with the electron in the first excited state. The electron-phonon interaction lifts the degeneracy and the first excited states get pinned to the ground state plus one phonon state as we increase the confinement frequency.