In this study, we have calculated energy levels of an N-electron quantum dot. For this purpose, we have used two different techniques, matrix diagonalization and quantum genetic algorithm, to obtain simultaneous solutions of the coupled Schrödinger and Poisson equation in the Hartree approximation. We have determined single particle energy levels, total energy, chemical potential and capacitive energy. We have also compared the results, demonstrated the applicability of QGA to many-electron quantum systems and evaluated its effectiveness. © World Scientific Publishing Company.