Based on the Continuum Damage Mechanics (CDM) theory, the progressive failure analysis of composite material duct dome is made. Combined with the stiffness degradation method, the ultimate bearing capacity and failure evolution of dome structure are studied from the perspective of material failure. The finite element model of composite material duct dome is established with APDL parametric language programming, and the analysis process is realized by multi-frame restart and arc-length method. According to Tsai-Wu failure criterion, the composite material damage and damage causes are judged, and the failure units are recorded continuously. The results show that: the matrix cracking failure mode appears first in the composite material dome structure, and at the moment a small amount of failure is of little effect on the overall dome structure performance; as the load continues to increase, the fiber fracture failure mode appears; when the fiber fracture occurs on a large scale, the nonlinear relationship of load-displacement becomes obvious gradually, and the structure performance declines sharply; there is almost no interface shear failure in the whole process. According to the structure load-displacement curve and failure unit number change, the Tsai-Wu failure factor when the dome is loaded is of theoretical and practical significance as the strength checking index of composite material duct dome.