Dropper is an important component of pantograph-catenary system employed in high-speed railway. The cyclic stress in dropper can lead to the fatigue failure during operation. The study of the fatigue life of dropper is the premise to ensure the safe exploitation of the train. The analytic vibration equation of dropper is proposed. Based on the finite difference method and MATLAB numerical calculation program, the vibration process and stress variation of the dropper are simulated. The influence of excitation frequency, vibration amplitude, and applied force on fatigue life of dropper is studied, according to the stress history of the dropper, the Basquin equation, and the Palmgren-Miner linear fatigue cumulative damage criterion. The numerical results show that the logarithm of the fatigue life of dropper shows a linear decreasing trend with the increase in the excitation frequency, vibration amplitude, or applied force.