In this paper, a comprehensive nonlinear damping prediction model of partially filled all-composite honeycomb-core sandwich panels (PF-ALHCSP) is proposed. Based on integrating high-order shear theory and Hamilton's principle, a theoretical model of the structure is established. Then, the energy equations are deduced by the finite element method. Thus, the nonlinear damping is obtained by the introduced complex modulus method. To validate the overall performance of the material and the accuracy of the theoretical model, the corresponding specimens are fabricated and a self-designed vibration testing platform is established. The results indicate that this material exhibits higher damping capacities compared to traditional metals or composite materials. To further enhance the material optimization, in conjunction with the proposed theoretical model, an investigation on the influence of three variables, filler density, honeycomb cell thickness, and panel thickness, on the structural damping characteristics across three different filling ratios is conducted. The proposed novel composite material and nonlinear damping prediction model can be adjusted according to practical applications for structural parameters, meanwhile effectively reducing material replacement frequency. The theoretical model provides a relatively accurate computational method for studying the nonlinear damping characteristics of partially filled foam honeycomb core sandwich structures, offering valuable insights for research in this field.