In an asymmetry quantum dot,the properties of the electron,which is strongly coupled with phonon,were investigated.The variational relations of the first internal excited state energy,the excitation energy and the frequency of transition spectral line between the first internal excited state and the ground state of the electron which is strongly coupled with phonon in an asymmetry quantum dot with the transverse and longituainal effective confinement length of quantum dot and the electron-phonon coupling strength were studied by using a linear combination operator and the unitary transformation methods.Numerical calculations for the variational relations of the first internal excited state energy,the excitation energy and the frequency of transition spectral line between the first internal excited state and the ground state of the electron which is strongly coupled with phonon in an asymmetry quantum dot with the transverse and longituainal effective confinement length of quantum dot and the electron-phonon coupling strength were performed and the results show that the first internal excited state energy,the excitation energy and the frequency of transition spectral line between the first internal excited state and the ground state of the electron which is strongly coupled with phonon in an asymmetry quantum dot will strongly increase with decreasing the transverse and longitudinal effective confinement length.The first internal excited state energy of the electron which is strongly coupled with phonon in an asymmetry quantum dot will decrease with increasing the electron-phonon coupling strength.The excitation energy and the frequency of transition spectral line between the first internal excited state and the ground state of the electron which is strongly coupled with phonon in an asymmetry quantum dot will increase with increasing the electron-phonon coupling strength.