The influence of an electrical current on the propagation of magnetostatic surface waves is investigated in a relatively thick (40 nm) permalloy film both experimentally and theoretically. Contrary to previously studied thinner films where the dominating effect is the current-induced spin-wave Doppler shift, the magnetic field generated by the current (Oersted field) is found to induce a strong nonreciprocal frequency shift which overcompensates the Doppler shift. The measured current-induced frequency shift is in agreement with the developed theory. The theory relates the sign of the frequency shift to the spin-wave modal profiles. The good agreement between the experiment and the theory confirms a recent prediction of a counterintuitive mode localization for magnetostatic surface waves in the dipole-exchange regime.