One of the important processes in structural design is the joining technique. Failure of composite joints involves different failure mechanisms depending upon the joining technique. In this study, a progressive failure analysis was performed on adhesively, riveted, and hybrid bonded double-lap joints. In the joints, a woven-type fiberglass-reinforced composite material was used as the main material; AV 2015 was used as the adhesive, and steel as the rivet material. The analyses were performed using ANSYS 12.1 finite element package software via software written using parametric design language (APDL) codes. At the end of the progressive failure analysis, failure loads and failure modes were determined for 30-, 45-, and 60-mm overlap lengths in accordance with the Maximum Shear Stress Theory and Hashin Criteria. For 45-mm overlap lengths, the joint strength of hybrid joints proved to be 2.72 and 1.145 times higher, respectively, than adhesive and fastening joints. Results showed that the failure load of the joint increased when the overlap length increased. In riveted joints, the failure occurring in the composite plates began around the rivet hole and the catastrophic failure of these types of joints resulted from fiber tensile failure.