Based on the band structure and related theoretical model of two-dimensional electron gas (2DEG), the dependence of the distribution of 2DEG on the thickness of ZnMgO barrier and related Mg content in ZnMgO/ZnO heterostructures has been computed by self-consistently solving the coupled Schrodinger and Poisson equations. Computation results reveal a critical thickness of the ZnMgO barrier for 2DEG formation, with no 2DEG occurring as the barrier thickness is below the critical value. When the thickness is above the value, the density of the 2DEG increases linearly with the thickness of ZnMgO barrier and saturates finally. The density of the 2DEG also shows a strong dependence on the Mg content in the ZnMgO barrier, with an obvious increase obtained as the Mg content enhances. At the same time, we compare the computed results with experimental data reported in the references with a certain degree of consistence obtained. Explanations and discussions of the above comparison have been presented in the study from the views of polarization effects and band structure.