Enhancing the stiffness of high-porosity honeycomb sandwich panels is a critical research field. To address this issue, a novel improved star-shaped honeycomb sandwich panel (SP-ISH) is designed by replacing the sharp corners with cubic struts and elongating the inclined ribs of the traditional star honeycomb. To fill the gap between global behaviors and local field distribution, an asymptotic analysis of the energy functional stored in periodic unit cells is performed. Based on the obtained effective plate properties, a two-dimensional equivalent downscaling model (2D-EDM) is developed and validated through comprehensive comparisons with results from 3D-printed experiments and 3D FE models, including assessments of static displacement, global buckling, and local field distribution. Furthermore, the effects of material and structural parameters on the effective plate properties and static performance are systematically investigated. The results reveal that the slenderness ratio of the rib and the core height-width ratio have the strongest influence on the equivalent tensile stiffness and bending stiffness, respectively. Notably, the SP-ISH outperforms other star-shaped honeycomb panels in specific stiffness, deformation resistance, and buckling load capacity due to the extended ribs and added struts. The study’s findings provide valuable insights for future designs and applications of this honeycomb structure.