The mean number of phonons of strong-coupled polaron in a parabolic quantum well is investigated by using the variational method combing the linear combination operator and unitary transformation. The relationships among the mean number of phonons of strong-coupled polaron in a parabolic quantum well, confinement strength of quantum well and electron-longitudinal optical phonons coupling strength are derived. Results show that the mean number of phonons of the strong-coupled polaron increases with increasing of quantum well confinement strength and electron-longitudinal optical phonons coupling strength. The mean number of phonons tends to be result of the crystalline material wit decreasing of the quantum well confinement strength. The interaction of the electron and phonons is enhanced with increasing of the confined strength and coupling strength of parabolic quantum well.