The energy levels, wave functions and the second-order nonlinear susceptibilities are calculated in GaAs/Al_0.2Ga_0.8As/Al_0.5Ga_0.5As asymmetric quantum well (AQW) by using an asymmetric model based on the parabolic and non-parabolic band. The influence of non-parabolicity can not be neglected when analyzing the phenomena in narrow quantum wells and in higher lying subband edges in wider wells. The numerical results show that under double resonance (DR) conditions, the secondorder difference frequency generation (DFG) and optical rectification (OR) generation susceptibilities in the AQW reach 2.5019 μm/V and 13.208 μm/V, respectively, which are much larger than those of the bulk GaAs. Besides, we calculate the absorption coefficient of AQW and find out the two pump wavelengths correspond to the maximum absorption, so appropriate pump beams must be selected to generate terahertz (THz) radiation by DFG.