Influences of the Coulomb field on the vibrational frequency and the mean number of optical phonons of weak-coupling impurity bound magnetopolaron in a parabolic quantum dot are studied using the linear-combination operator and the unitary transformation method. Expressions for the vibration frequency and the mean number of optical phonons of weak-coupling impurity bound magnetopolaron in a parabolic quantum dot as a function of the effective confinement length of quantum dot, the Coulomb bound potential and the cyclotron resonance frequency of magnetic field are derived. Numerical calculations are performed and the results show that the vibration frequency and the mean number or optical phonons of the weak-coupling impurity bound magnetopolaron in a parabolic quantum dot increase rapidly with decreasing of the effective confinement length of quantum dot, and increase with increasing of the cyclotron resonance frequency of magnetic field and the Coulomb bound potential. These can be attributed to the interesting quantum size effects.