Carbon fiber reinforced polymer (CFRP) with high specific strength, specific modulus, and other outstanding properties, which could be used in aerospace, shipbuilding, and railway. The joint of carbon fiber composite material plate and metal material plate plays an important role in the overall performance of the structure. In this paper, a carbon fiber reinforced polymer (CFRP) progressive damage model is developed based on composite laminate theory and 3D Hashian theory. The model of the double bolt single lap joint shear connection is established for the CFRP plate and the finite element method is used to carry out the stress analysis and failure prediction of the lap structure. The effect on structural performance under tensile conditions was studied through the change of double bolt spacing. The results show that the decrease in bolt row spacing can lead to the interference effect between holes. In addition, the progressive damage of the composite plate is located near the center line of the bolt hole.