Dynamic Mine disasters can be induced by the instability and failure of a composite structure of rock and coal layers during coal mining. Coal seam contains many native defects, severely affecting the instability and failure of the compound structure. In this study, the effects of coal persistent joint on the strength and failure characteristics of coal-rock composite samples were evaluated using PFC2D software. The results show that with the increase of included angle α between the loading direction and joint plane direction, the uniaxial compressive stress (UCS) and peak strain of composite samples first decrease and then gradually increase. The elastic moduli of composite samples do not change obviously with α. The peak strain at α of 45° is the lowest, and the UCS at α of 30° is the smallest. This is inconsistent with theoretical analysis of lowest UCS at α of 45°. This is because that the local stress concentration caused by the motion inconformity of composite samples may increase the average axial stress of upper wall in PFC2D software. Moreover, the coal persistent joint promotes the transformation from the unstable crack expansion to the macro-instability of composite samples, especially at α of 30° and 45°. The majority of failures for composite samples occur within the coal, and no obvious damage is observed in rock. Their failure modes are shear failure crossing or along the coal persistent joint. The failure of composite sample at α of 30° is a mixed failure, including the shear failure along the persistent joint in coal and tensile failure of rock induced by the propagation of coal persistent joint.