A passive double triangular damping (DTD) device with equivalent negative stiffness is proposed in this study. The DTD device consists of transmission systems and triangular damping systems. A mechanical model was developed to describe the force–displacement relationship of a triangular damping system, while the feasibility of both the system and model was evaluated using experimental tests. The theoretical analysis demonstrated that DTD was a form of damping with equivalent negative stiffness, and the equivalent expressions were generated. Finally, the prospect of application in the DTD-controlled isolation system was explored using numerical simulation. The results revealed that DTD was more effective than a lead–rubber bearing in reducing isolator displacement and rooftop acceleration when subjected to ground motions.