Mutilayered thin (Ba0.80Sr0.20)(Ti1-xZrx)O3 (BSTZ) films with various compositional graded layers (CGL) have been successfully fabricated on Nb doped SrTiO3 substrates by pulsed-laser deposition technique with four BSTZ ceramic targets (x=0.36,0.18,0.08,0). The gradients of compositions are artificially tailored in multilayered thin films by varying the CGL, and x-ray diffraction indicates that the internal stress is modulated in the multilayered films. Influence of the composition gradient on the dielectric properties has been investigated at the temperature range from 120 to 440 K. Temperature stability of permittivity of the multilayered films is found to be improved with the increase of the gradients of compositions. Moreover, a dielectric relaxation process with activation energy of 1.02 eV is observed, which is also related to the composition gradient, and can be described to motion of oxygen vacancies. The results show that the temperature stability of permittivity can be tailed by the design of multilayered film with CGL, and the internal stress induced by the gradients of composition could influence the relaxation process.