In the framework of effective mass envelope function approximation, the impurity states in GaN  /  Al_xGa_{1  −  x}N spherical quantum dot (QD) are calculated by plane-wave expansion method. The binding energies of the impurity in 1s and 2p± states and the transition energy between 1s state and 2p± state are calculated and analyzed in detail. Several critical influencing factors of impurity states, including geometry, impurity position, material composition, and applied electric field, are considered in the calculation. The effects of QD radius, the impurity position, and the electric field strength on binding energies of 1s state and 2p± state are different. However, the effect of Al component on binding energies of 1s state and 2p± state is consistent. The transition energy is strongly dependent on the QD radius, impurity position, Al composition, and electric field strength. The change trend of transition energy is similar to that of binding energy in 1s state.