The binding energy and Stark effect energy shifts of a shallow donor impurity state in a strained GaN/Al_xGa_1-xN spherical finite-potential quantum dot (QD) are calculated using a variational method based on the effective mass approximation. The binding energy is computed as a function of dot size and hydrostatic pressure. The numerical results show that the binding energy of the impurity state increases, attains a maximum value, and then decreases as the QD radius increases for any electric field. Moreover, the binding energy increases with the pressure for any size of dot. The Stark shift of the impurity energy for large dot size is much larger than that for the small dot size, and it is enhanced by the increase of electric field. We compare the binding energy of impurity state with and without strain effects, and the results show that the strain effects enhance the impurity binding energy considerably, especially for the small QD size. We also take the dielectric mismatch into account in our work.