This paper calculates the time evolution of the quantum mechanical state of an electron by using variational method of Pckar type on the condition of electric-LO-phonon strong coupling in a parabolic quantum dot. It obtains the eigenenergies of the ground state and the first-excited state, the eigenfunctious of the ground state and the first- excited state This system in a quantum dot may be employed as a two-level quantum system qubit. The superposition state electron density oscillates in the quantum dot with a period when the electron is in the superposition state of the ground and the first-excited state. It studies the influence of the electric field on the eigenenergies of the ground state, the first-excited state and the period of oscillation at the different electron-LO-phonon coupling constant and the different confinement length.