Abstract: Mesh generation is a crucial preprocessing step for mesh-based numerical methods such as finite element analysis. To address the issues of excessive iterations and high costs associated with existing Voronoi diagram or pow-er diagram-based methods when generating anisotropic meshes, this paper proposes a variational generation method centered on mesh vertices and their connectivity, which defines the error between the original function and its piecewise linear approximation as an energy function, and minimizes it through iterative optimization to generate the mesh result. To ensure that mesh elements maintain convexity, the gradient of the energy function with respect to mesh vertices is derived, and vertex positions are optimized within a constructed safe region. Subsequently, the connectivity is optimized based on the energy descent principle, where a forced short-edge flipping strategy is introduced to search for superior local optima, and an alternating optimization strategy is employed to update vertex positions and connectivity iteratively. Compared with Optimal Voronoi Tessellation (OVT) and Optimal Power Diagram (OPD) methods, the results of the proposed method demonstrate higher quality in terms of mesh element aspect ratio and corrected area metrics, and the number of iterations is reduced by 90% compared to the OPD method.