Quantum oscillations of nonlinear resistance are investigated in response to electric current and magnetic field applied perpendicular to single GaAs quantum wells with two populated subbands. At small magnetic fields current-induced oscillations appear as Landau-Zener transitions between Landau levels inside the lowest subband. Period of these oscillations is proportional to the magnetic field. At high magnetic fields different kind of quantum oscillations emerges with a period,which is independent of the magnetic field. At a fixed current the oscillations are periodic in inverse magnetic field with a period that is independent of the dc bias. The proposed model considers these oscillations as a result of spatial variations of the energy separation between two subbands induced by the electric current.