Based on the pseudopotential scheme, the electronic and positron properties of zinc-blende compounds MgTe, CdTe and their alloy MgxCd1-xTe alloy have been studied. The agreement between our calculated electronic band parameters and the available experimental data is reasonable. For the ternary alloy MgxCd1-xTe, the virtual crystal approximation is coupled with the pseudopotential method. The energies at Γ, X and L points of MgxCd1-xTe alloy as a function of the alloy concentration are calculated. The electronic and positron band structures derived from pseudopotential calculations are also reported. Other quantity such as ionicity factor by means of our model with respect to the alloy concentration is discussed.