Influence of the phonon dispersion on the properties of the weak-coupling polaron in a parabolic quantum dot was investigated by using the linear combination operator and unitary transformation method. Taking account of the longitudinal optical (LO) phonons dispersion in a parabolic approximation, the ground state energy and the self-trapping energy of the polaron in a parabolic quantum dot as a function of the effective confinement length of the quantum dot, the electron-LO-phonon coupling constant and the coefficient of the phonon dispersion were obtained. Numerical calculation results show that the ground state energy decreases with the coefficient of the phonon dispersion increasing, the self-trapping energy increases with increasing the coefficient of phonon dispersion.