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Shell-model molecular dynamics method is used to study the melting temperatures of MgO at elevated temperatures and high pressures using interaction potentials. Equations of state for MgO simulated by molecular dynamics are in good agreement with available experimental data. The pressure dependence of the melting curve of MgO has been calculated. The surface melting and superheating are considered in the correction of experimental data and the calculated values, respectively. The results of corrections are compared with those of previous work. The corrected melting temperature of MgO is consistent with corrected experimental measurements. The melting temperature of MgO up to 140GPa is calculated.