The electric field effects on bound polarons in polar quantum wires with a finite confining potential are studied by a variational method. Both the confined bulk longitudinal optical phonons and the interface optical phonons are taken into account in considering the electron-phonon as well as the impurity-ion phonon couplings. The binding energies are calculated as functions of the transverse dimension of the quantum wire, and the donor-impurity position for different electric fields. The numerical results for the GaAs quantum wire are given and discussed as an example. A peak of the binding energy is found at a certain radius and shift toward a larger radius with applying an electric field. The calculated results confirm that the electron-phonon interaction reduces both the binding energies of impurity states and the Stark shifts and cannot be neglected.