We calculate the effects of dielectric mismatch on shallow donors and acceptors in a spherical GaAs-Al_1-xGa_xAs quantum dot for both a finite barrier and an infinitely high barrier using the variational approach. The results have shown that the addition of dielectric mismatch enhances impurity binding energies considerably, especially when the radius of the quantum dot is small. The results also showed that the effects of dielectric mismatch on donors are comparable with those on acceptors, and the corresponding effects for an infinitely high barrier are larger than for a finite barrier.