In the effective mass approximation, we calculated the wave functions and some energy states of helium and helium-like quantum dots (QDs) with impurity charges Z = 0, 1, 2, 3, and 4. In addition, we carried out the ionization energies of these QDs as a function of dot radius, and we investigated the influence of impurity on the ionization energy. We utilized the method that is a combination of quantum genetic algorithm (QGA) and Hartree-Fock Roothaan (HFR). The results are in a good agreement with literature results. © 2011 Wiley Periodicals, Inc.