Dropper is the key component of in a catenary system and it is prone to fatigue fracture. Dropper stress directly affects the operation safety of high-speed railway. In this paper, a span of dropper in a catenary system is modeled to investigate the effects of contact wire tension on dropper stress. The response equation of contact wire and the theoretical equation of dropper stress are deduced. The initial and boundary conditions of each dropper are determined, and then the stress of each dropper is calculated by the finite difference method using a MATLAB program. The results show that the stress amplitude and the maximum tensile stress of the dropper decrease significantly with the increase of contact wire tension. When the tension is low, the stress changes of dropper near the load location experience three stages: instant rebound, attenuated vibration, and bending compression. However, the attenuation vibration stage disappears when the tension is increased to a certain extent. Therefore, the control of the vibration response of the contact wire can effectively reduce the stress amplitude and the maximum tensile stress of the dropper, so as to improve the working reliability of the dropper.