Laminated composite bolted joints are increasingly used in the aerospace field, and their damage and failure behavior has been studied in depth. In view of the complexity and stability requirements of laminated composite bolted structures, accurate prediction of damage evolution and failure behavior is significant to ensure the safety and reliability of the structures. In this paper, a novel asymptotic damage model is developed to predict the damage process and failure behavior of laminated composite bolted joints. In this model, the modified Puck criterion and the maximum shear stress criterion are used for fiber yarns. The parabolic yield criterion is adopted for the matrix, and the fiber fracture, inter-fiber fracture and matrix fracture are considered at the microscopic level. The pull-out strength and progressive failure behavior of countersunk and convex bolted joints structures are predicted by using the proposed model, and the corresponding experimental studies are carried out. The results show that the prediction results are in good agreement with the experimental data, which verifies the reliability of the model. Additionally, the effects of different structural parameters (thickness and aperture) on the progressive damage and failure behavior during pull-out is analyzed by the proposed model, and correction factors of pull-out strength are obtained, which provides a powerful tool for the design, analysis and progression of laminated composite bolted joint structures.