[Purposes] This paper aims to study the seismic performance of single-tower cable-stayed bridges with asymmetric steel-concrete hybrid girders and explore the differences in seismic response of asymmetric structures. [Methods] Midas Civil software was used to establish a finite element model of the entire cable-stayed bridge with asymmetric steel-concrete hybrid girders based on the West Branch Channel Bridge of Changsha Xiangluzhou Bridge. The seismic response analysis was conducted using the response spectrum method and the nonlinear time history analysis method, respectively. The impact of structural asymmetry on the seismic performance of auxiliary piers, transition piers, and pile foundations of the cable-stayed bridge was mainly studied. [Findings] The dynamic characteristics and seismic response of the single-tower cable-stayed bridge with asymmetric steel-concrete hybrid girders exhibit significant asymmetry. There are significant differences in the internal force response of the two transition piers and two auxiliary piers arranged asymmetrically under seismic action. The structural asymmetry is more sensitive to lateral earthquakes and should be taken seriously in seismic design. Except for the pile foundations of the two transition piers, the structural dimensions and reinforcement forms of Changsha Xiangluzhou Bridge designed according to static calculation can meet the seismic performance goals under various earthquake conditions. The safety reserves of tower and pier bodies under lateral and vertical seismic actions are greater than those under longitudinal and vertical seismic actions, while the safety reserves of pile foundations under lateral and vertical seismic actions are almost all smaller than those under longitudinal and vertical seismic actions. Due to the influence of structural asymmetry, the pile foundation of the 27# transition pier of the side span always fails before that of the 31# transition pier of the main span. Under lateral seismic action, there are significant differences in the seismic axial force of each row of pile foundations affected by the bearing platform. [Conclusions] From the perspective of economy and seismic rationality, differentiated seismic design should be carried out for single-tower cable-stayed bridges with asymmetric steel-concrete hybrid girders. The research results can provide a useful reference for the seismic design of asymmetric cable-stayed bridges and other asymmetric bridge structures.