The binding energy of a hydrogenic donor in a spherical GaAs-Ga1- x Al x As quantum dot with parabolic confinement is calculated by taking into account the finite value of the barrier potential. Using the effective-mass approximation, we obtained the energy of the ground state as a function of the dot size for different impurity positions. The results show that the effect of the finite value of the barrier potential is to lower the energies of the states. The differences between the proper solutions and the infinite barrier potential approximation increase noticeably, especially for on-center impurity and for small dot radii. We have also shown that the impurity binding energy is much dependent upon the impurity position in the system. This fact is important for a correct description of impurity-related absorption and photoluminescence experiments.