The electron mobility characteristics of a ZnMgO/ZnO heterostructure are systematically investigated by an ensemble Monte Carlo method. Screening effects are included in all electron scattering mechanisms. The mobilities are calculated for a temperature range of 4 to 300 K and Mg contents ranging from 8.5 to 44%. In this range, dislocation scattering (DS) and interface roughness scattering (IFR) are highly effective for low and high values of Mg compositions, respectively. Screening effects must be considered in scattering mechanisms to achieve a reasonable agreement with existing experimental results. Our findings could be significant for the design and optimization of ZnO-based devices.