We study low temperature electron transport mobility μn in a GaAs∕InxGa1−xAs double quantum well structure. Both the extreme barriers are δ doped with Si so that the electrons diffuse into the adjacent wells (InGaAs layers) forming two sheets of two-dimensional electron gas separated by a thin central barrier. The subband electron wave functions and energy levels of the coupled quantum well system are obtained numerically as a function of well width and barrier width. We have considered the effect of alloy disorder scattering and impurity scattering on μn. The screening of the scattering potentials by the 2D-electrons is obtained in terms of the static dielectric response function within the random phase approximation. The effect of screening on the alloy disorder potential, which has been normally neglected due to short range nature of the potential, has been analyzed. We have also studied the effects of the intersubband scattering and coupling of wave functions through the barrier on μn for the multisubband system.