It is well known that at low temperatures the acoustic-phonon limited mobility of a two-dimensional electron gas in GaAs heterostructures is determined predominantly by piezoelectric scattering. We suggest a way of significantly enhancing of the acoustic-phonon limited mobility by reducing piezoelectric scattering via inserting thin metal layers at finite distances from the electron channel. As an example, for a GaAs quantum well of 100Å width placed between two metal layers and separated from them by 50Å, the mobility at T=0.2K increases by about 10 times. Moreover, the mobility increases several times when only one metal layer or highly doped semiconductor is placed near a narrow well.