Compositional graded thin films of (Ba0.8Sr0.2)(Ti1-xZrx)O3 (BSTZ) are grown on MgO by pulsed laser deposition technique with four BSTZ ceramic targets. Gradients of composition are achieved by artificially tailoring composition in multilayered thin films to form compositional graded layers (CGL). In each CGL four individual layers of BSTZ with x = 0.36, 0.18, 0.08 and 0 are grown^in series with equal thickness. Three kinds of CGL samples comprising one, two or four CGLs have been elaborated with the same total thickness by varying the thickness of each CGL. Raman spectra show existence of tetragonal structure in all the multilayered BSTZ thin films. Raman peak at 535 cm-1 shifts to high frequency with increasing of compositional gradient, and the peak at 750 cm-1 also shows a small shift to high frequency. Moreover, other Raman peak is observed at about 830 cm-1, which is associated with phonon mode of cubic phase, and such peak shifts towards lower frequency with increasing of compositional gradient. The shift of Raman peak is related to variation of internal stress in BSTZ thin film due to increasing compositional gradient.