In this paper, a simple chain suspension catenary model is constructed. The acting force of pantograph is reduced to a displacement loading. The stress and fatigue life of railway catenary dropper incorporating displacement loading and fluctuating wind load are studied. Through writing a MATLAB code, the vibration equation of the dropper is used to calculate its stress under different conditions using a finite difference method, combining with the initial boundary value conditions obtained by the response equations of the contact wire. Based on the dropper stress, its fatigue life can be obtained. The results show that under the 250 km/h train speed, the stress change process of the dropper experiences three stages: immediate rebound, attenuation vibration, and bending compression. Dropper Ⅳ is most likely to break in a span. Compared with dropper Ⅳ, the fatigue life of dropper Ⅰ is 11 times, and those of droppers Ⅱ, Ⅲ, and Ⅴ are about 2.5 times. Compared with no wind, the fatigue lives of droppers Ⅰ-Ⅳ are reduced by approximately three times at a wind speed of 25 m/s. This work provides a powerful means for the study of dropper stress under actual working condition.