We analyze the asymmetric doping-dependent electron mobility mu of GaAs/InGaAs/GaAs quantum well field-effect transistor (QWFET) structure. We consider doping concentrations, nd1 and nd2, in the substrate and surface barriers, respectively, and study mu as a function of nd2, taking (nd1 + nd2) unchanged. An increase in nd2 decreases nd1, yielding interesting changes in the occupation of subbands. For well width W < 164 & Aring;, mu is due to single subband occupancy (SSO). Around W = 164 & Aring;, there occurs first SSO, then double subband occupancy (DSO), and again SSO with an increase in nd2. Near the transition of subbands, abrupt discontinuities in mu arise due to inter-subband effects. Thus, high to low and then high values of mu are obtained, displaying almost flat-like variations, symmetric about |nd2 - nd1| = 0. As W becomes wider, complete DSO occurs throughout the range of nd2 having reduced mu. Alternatively, keeping nd1 unchanged and by increasing nd2,mu raises due to enhanced N-s, with a drop near the transition from SSO to DSO. Under SSO, mu is controlled by the ionized impurity and alloy disorder scatterings, while under DSO, the impurity scattering determines mu. Our analysis on mu can help to examine the inter-subband effects on device characteristics of the QWFET system.