The effect of the electric field on the binding energy of the ground state of a shallow donor impurity in a graded GaAs quantum-well wire (GQWW) was investigated. The electric field was applied parallel to the symmetry axes of the wire. Within the effective mass approximation, we calculated the binding energy of the donor impurity by a variational method as a function of the wire dimension, applied electric field, and donor impurity position. We show that changes in the donor binding energy in GQWWs strongly depend not only on the quantum confinement, but also on the direction of the electric field and on the impurity position. We also compared our results with those for the square quantum-well wire (SQWW). The results we obtained describe the behavior of impurities in both square and graded quantum wires.