On the condition of electron-LO phonon strong coupling in a parabolic quantum dot, the eigenenergies and eigenfuctions of the ground state and first excited state using variational method of Pekar type were obtained. The system in quantum dot may be employed as a two-level quantum system qubit. The relations on the electron-LO phonon strong coupling, the confinement length with the electron probability density were investigated. The results indicate that the electron probability density increases with increasing the electron-LO phonon strong coupling and decreasing the confinement length. The results are meaningful for preparing a qubit.