<p>This study focuses on a reasonable lateral isolation system for a typical long-span single-tower cable-stayed bridge with a significantly asymmetric span arrangement that is particularly suitable for mountainous areas. Based on the Jinsha River Bridge, the significant structural asymmetry and its effects on structural seismic responses were analyzed. The significantly asymmetric characteristics could result in complex dynamic behavior in seismic conditions and the lateral seismic responses of the structure are governed by multiple modes. A multilinear model composed of an ideal elastoplastic element and a multilinear elastic element was used to simulate different hysteresis, and a parametric analysis was conducted to investigate the appropriate damping hysteresis for the lateral seismic isolation of such a bridge. It shows that the inverted S-shaped hysteresis has relatively smaller secant stiffness and could help to balance the great difference in the lateral stiffness of the tower/piers. Thus, the inverted S-shaped hysteresis could lead to more efficient damping effects and less base shear forces of the tower/piers. A correlation between the reasonable yield forces of the dampers in the lateral isolation system, determined through an influence matrix-based method, and the shear forces of the corresponding bearings in the lateral fixed system was also observed. Moreover, the influence of geological conditions including different terrain and site conditions on the reasonable lateral isolation system was further investigated. It suggests to use dampers at all tower/pier locations when the side span crosses a steep valley slope, while a lateral isolation system without using dampers at the auxiliary piers could be employed when the side span crosses a gentle valley slope. Soft sites require larger damper yield forces and cause greater seismic responses compared to hard sites.</p>