The crack in adhesives is one of the common damage patterns in composite adhesive structures, which will affect the integrity of composite structures. In this paper, the single-lap bonded composite joints which are the common adhesive structures in aircrafts were chosen as the study object. The three-dimensional numerical model was established with the bilinear cohesive constitutive relation characterizing the static crack propagation, and then the static model was extended to fatigue crack propagation model. The distribution of stress and strain, crack propagation and failure mechanism were studied by combing the experiment and numerical methods. The results have shown that the strain of single-lap adhesive joints varies nonlinearly under static and fatigue loadings because of the eccentric tension. Due to the stress concentration, fatigue cracks appear on both ends of the lapped area firstly, and then extend to the central area until cover the whole lapped area. The static failure mode is cohesive failure, and the interface debonding failure is observed in fatigue fracture.