We analyze the structural-asymmetry-induced nonlinear enhancement of the electron mobility μ in a GaAs/InxGa1−xAs double-quantum-well pseudomorphic high-electron-mobility transistor (p-HEMT). We consider the well widths wi and ws and the doping concentrations ndi and nds in the barriers along the substrate (inverted doping) and surface (surface doping), respectively. We show that for a suitable choice of ws and nds, the variation of wi leads to interesting changes in the occupation of subbands, i.e., first, single-subband, then double-subband, and again, single-subband occupancy. By increasing ndi, the range of double-subband occupancy is enhanced. However, the lowering of μ due to the inter-subband effects is minimized. In the case of a single-channel HEMT, i.e., say, for ndi = 0, only a single subband is occupied. The mobility exhibits a cusplike behavior with a minimum at a certain value of wi. If one takes a higher value of nds, the occupation of subbands shows a different trend, i.e., from single- to double-subband occupancy as a function of wi for different ndi values with nonmonotonic variations of μ. Our results of the nonlinear enhancement of mobility can be utilized for the analysis of the coupled GaAs/InxGa1−xAs double-quantum-well p-HEMT structure.