The effects of the image potential on hydrogenic impurity binding energies in quasi-one-dimensional GaAs/AlAs quantum well wires with a rectangular cross section are investigated. The results have shown that, when the impurity ion image potential is considered, the variations in binding energy are considerable and, when the impurity ion and electron image potentials are considered simultaneously, the corresponding variations in binding energy are small. The results also showed that the image potential is important, especially when the cross section dimensions of the quantum wire become small.