Abstract: The effect of gravitational waves (GW) on phonon in axisymmectic non-uniform elastic medium is analysed by means of the complex coordinate in Serebryany's complex space. and expression of diving force produced by the GW and corresponding phonon soluitons are given. In our solution forms. they are shown that the GW propagating along symmetric axial direction generates only perturbation to radial and tangential components of the phonon fields. while the GW propagating along direction perpendicular to the symmetric axis generates perturbation to all components of the phonon fields. i.e., radial, tangential and axial components. The strength of pertur-bation depends on concrete form of radial distribution function of shear modulus and the GW's amplitude. Moreover, above results are compared with the GW's perturbing effect in topological phonon space with the spiral dislocation.