Based on resonant subband transitions, the second-order and third-order nonlinear optical effects in an asymmetric quantum well (AQW) with the structure of GaAs/Al0.2Ga0.8As/Al0.5Ga0.5As have been theoretically investigated on the conditions of parabolic and non-parabolic bands. With the increase of two pump wavelengths λp1 and λp2 separately, the second-order nonlinear difference frequency susceptibility χ(2)DFG and the two third-order nonlinear susceptibilities χ(3)ω1 and χ(3)ω2 increase to a maximum value, and then drops down rapidly. In comparison with the condition of parabolic subband, the curves of χ(2)DFG, χ(3)ω1 and χ(3)ω2 show obvious red-shift as a function of the short pump wave λp1 on the condition of nonparabolic subband. However, with the increase of long pump wave λp2, no changes of peak position have been discovered. The physical origin of all red-shift in nonlinear optical effects is the different energy level gaps on the two conditions of subband, which causes the changes in resonant condition. The primary reason for different peak values is the different transition matrix elements, and the other reason is energy level gaps.