Designing a numerical scheme that can preserve the geometric structure for anisotropic geometric flows with an arbitrary anisotropic surface energy is a long-standing problem. In this talk, we propose a structure-preserving parametric finite element methods (SP-PFEM) for the anisotropic mean curvature flow and anisotropic surface diffusion, which preserve the geometric structures at the full-discretized level. The SP-PFEM innovates with a surface energy matrix and the Cahn-Hoffman ξ-vector, leading to a new geometric identity for dealing with the anisotropic effect. This new geometric identity further allows our SP-PFEM to be extended to other geometric flows with anisotropic effects.