In this paper, the system of the electron-bulk LO-phonon interaction in a quantum well within constant electric and magnetic fields along the growth axis, is analysed by the method of variational wave-function and harmonic oscillator operator algebra. The representation of the ground state energy which includes the correction of the second-order perturbation is obtained as a funtion of the electron-LO-phonon coupling constant, the width of the quantum well, the strength of the electric and magnetic field. The results have shown that, the polaronic correction to electron ground state energy reduces with increasing well width and electric field, but enhances with increasing magnetic field.