Abstract <p>The effect of screening of the Coulomb potential of impurity ions on the electrical conductivity (EC) of a two-dimensional degenerate electron gas in a semi-parabolic quantum well is studied. The dependences of EC on the quantum well parameters, such as the width and potential of the quantum well, and also on the conduction electron concentration, and the number of subbands in the case of scattering by distant and background impurity ions are determined. It is established that, as the quantum well width decreases, EC increases significantly in the case of scattering by background ions and increases in the magnitude and, changing the sign, becomes negative in the case of distant ions. This increase is due to the effect of electron localization and a decrease in the electron scattering. It is found that, as the quantum well potential increases, the relative EC increases in magnitude and becomes negative in the case of scattering by distant ions and increases linearly without change in the sign in the case of scattering by background ions. As the conduction electron concentration increases, EC increases, and it increases the faster the higher is the potential. In the case of scattering by distant impurity ions, EC becomes negative at small numbers of the subbands, and the EC magnitude increases as the number of the subbands increases. In the case of scattering by background ions, EC is shown to have a minimum at small numbers of the subbands, and it increases monotonically as the number of the subbands increases.</p>