This paper reports that the ground-state energy of polaxon was obtained with strong electron-LO-phonon coupling by using a variational method of the Pekax type in a parabolic quantum dot. Quantum transition is occurred in the quantum system due to the electron-phonon interaction and the influence of temperature. That is the polaxon transit from the ground-state to the first-excited state after absorbing a LO-phonon and it causes the change of the polaxon lifetime. Numerical calculations are performed and the results illustrate that the ground-state lifetime of the polaron will increase with increasing the ground-state energy of polaxon and decrease with increasing the electron-LO-phonon coupling strength, the confinement length of the quantum dot and the temperature.