Abstract: A set of gradient stress was obtained by solving the elastic mechanical equations and used to Landau thermodynamic theory to explain the diffuse dielectric anomaly of BaTiO3 film grown on a tensile substrate. The results predict that a and aaphase may coexist in the film. The hysteretic spontaneous polarization behavior of the film can not be revealed for the inplane polarization exists for the two phases. The temperature dependence of outplane dielectric constant agrees with the experimental result.