The influence of Coulomb field on the properties of the excited state of weak-coupling polaron in an asymmetric quantum dot was studied by the linear combination operator and unitary transformation method. Relations of vibrational frequency, the first excited state energy of weak-coupling polaron in an asymmetric quantum dot with effective confinement length of quantum dot, Coulomb bound potential of weak-coupling polaron in an asymmetric quantum dot are obtained. It is shown by evaluating numerically that the vibrational frequency, the first internal excited state energy increase rapidly with the effective confinement length decreasing when the Coulomb bound potential is determined, and the vibrational frequency increases with the Coulomb bound potential increasing, the first internal excited state energy has minimal value with the Coulomb bound potential increasing when effective confinement length is determined.