The electron-transport properties of a ZnMgO/ZnO hetero structure were studied by use of an ensemble Monte Carlo technique. There was no intentional doping in the profile and the entire charge is because of polarization of charges at the interface. Interface roughness, and the intensity of acoustic and optic phonon scattering were used in the ensemble Monte Carlo method to find the transport properties of the two-dimensional electron gas (2DEG). The low-field mobility characteristics of the structure were determined as a function of temperature, the thickness of the ZnMgO layer, and the interface roughness. The interface roughness was found to have a very large effect on the drift mobility of carriers, especially at low temperatures. It was observed that as the thickness of the ZnMgO increases the concentration of electrons increases whereas the mobility of the electrons decreases. The low-field mobility values obtained from ensemble Monte Carlo simulations were in agreement with published experimental data.