The work aims to propose a multi-scale optimization design method of plate and shell damping composite structure to obtain a plate and shell structure with good anti vibration performance and ensure the normal operation of the equipment. Aiming at dynamic flexibility, a mathematical model of multi-scale problem was established under frequency domain excitation and fixed frequency point excitation. Macro distribution of damping materials and microstructure of plate and shell damping composite structure were collaboratively designed. The sensitivity of objective function and constraint conditions to design variables was derived, and the optimization mathematical model was solved based on the moving asymptote method. The proposed multi-scale design method can effectively obtain the optimal macro layout of damping materials and the optimal microstructure configuration of damping composites for plate and shell structures. It improved the structural dynamic performance. At the same time, the results also showed that the vibration response of the structure coated with damping composites was significantly reduced compared with that coated with only a single damping material. The research shows that the macro distribution of damping materials is different under different excitation frequencies. The damping materials are mainly distributed at the maximum displacement of the structural modal shape and the support end. By strengthening the structural stiffness, the structural deformation is restrained and the vibration response is reduced. The microstructure configuration is basically similar. Its basic morphology is that the distribution of low stiffness and high damping materials is strip-shaped. The strip-shaped damping composite microstructure has a large stiffness in the bending direction of the structure, which can effectively resist the bending deformation of the structure.