Double-sided self-pierce riveting (DSSPR) has great application potential in joining the same or dissimilar sheets due to its simplified die structure, high joining efficiency, and smooth joint surface. Previous studies have shown that changing rivet parameters, such as chamfered angle position, can improve joining strength, but the improvement effect is still relatively limited. In this paper, to significantly enhance the joining strength, a novel combined rivet structure was proposed and used in the DSSPR process of Al5052 sheets, and its effect on strength improvement and the underlying mechanism were investigated. Morphological change, strain, and stress distribution of the combined rivets during the joining process were investigated through experiments and numerical simulations. Tensile shear tests were conducted to compare the shear strength of the combined rivets and conventional rivets. Moreover, the failure behaviors of joints including macroscopic failure mode and microscopic surface morphology were analyzed, and the mechanism for combined rivets to enhance the joining strength was illustrated. Results showed that adopting the new combined rivets can significantly improve joint strength. Compared with a single conventional tubular rivet, the tensile shear strength and energy absorption of combined rivets can increase by up to 91% and 261%, respectively. Two types of failure modes were discovered according to the failure behaviors of sheets, which were characterized by the detachment of rivets and the tearing characteristics of the sheet. This paper provides a new approach for the rivet design and joining strength improvement strategy for the DSSPR process.