The drum-shaped honeycomb-type III cable dome with a quad-strut layout abandons the traditional concept, incorporating a multi-support pole concept, making it one of the most structurally diverse types of cable dome structures. Its upper chord cable mesh is evenly divided, resulting in a simple and efficient structural design. This design approach reduces the usage of cables and struts, making pre-stressing and tensioning construction more convenient. Furthermore, the structure exhibits good cost-effectiveness. Based on the node force equilibrium equations, a general formula is derived for calculating the internal forces of prestressed cables and struts in the prestressed state of the structure. Additionally, the variation of prestress distribution with geometric parameters of the cable dome structure is analyzed. A numerical model with a span of 120 meters was established in the general finite element software Ansys to investigate the influence of structural parameters on the structural natural frequency characteristics. Moreover, using the nonlinear dynamic analysis method, the dynamic response of the structure under multidimensional seismic loads was compared and analyzed. The research results indicate that the prestress distribution of the structure is reasonable, with a greater amount of prestress in the outer ring compared to the inner ring. This observation suggests that the stiffness of the structure is primarily supported by the outer ring structure. The structural natural modes of vibration predominantly exhibit vertical deformation, indicating that the vertical stiffness of the structure is weaker than the circumferential direction. Furthermore, when subjected to seismic loading, the internal forces in cables and struts, as well as the dynamic displacements of key nodes, are relatively small, demonstrating excellent seismic performance.