The modified Landau-Devonshire thermodynamic theory has been used to investigate the ferroelectricity of Pb(Zr0.7, Ti0.3)O3 film grown on MgO substrate. A set of gradient thermal stresses is imposed on the films. The stress-temperature diagram, the spontaneous polarization and the dielectric susceptibility at 25°C on the stress were computed. Structure transitions of first order can be driven by the stress. The mean of out-plane spontaneous polarization and dielectric susceptibility on the temperature were also predicted.