In this paper, structural and thermal properties of Zn1-xCdxO alloys for x=0, 0.125, 0.25, 0.375, 0.5, and 0.625 have been investigated by Ab initio calculations method. Both lattice constants a and c of wurtzite structure follow Vegard's law and are in a good agreement with the experimental data for x=0. The diagrams of specific heat at constant volume versus temperature for different values of x have been plotted and values of specific heat at constant pressure for different concentrations of x at 300K, 600K and 900K have been obtained. The value of specific heat at constant pressure for ZnO has a good consistency with experimental data. Specific heat at constant volume increased by increasing temperature and specific heat at constant pressure decreased by increasing x. The diagrams of Debye temperature versus x at 0K, 300K, 600K and 900K have been plotted, too. These diagrams state that Debye temperature decreases by increasing x or increasing temperature.