We experimentally study the parabolic negative magneto-resistance (NMR) in high density (Ns>1012cm−2) and low mobility (μ<103cm2/Vs) two-dimensional (2D) electron gas realized by δ-doping a narrow (5nm) AlGaAs/GaAs/AlGaAs quantum well. We show that the parabolic NMR in this 2DEG is well described by the theory which connects the parabolic NMR to the existing quantum logarithmic correction to the conductivity of the 2D electron system in the case of the diffusive transport.