Abstract: The superconducting electrodynamic suspension maglev train may experience risks of the excessive suspension gap variation, car body acceleration, and stationarity during high-speed operation due to the external excitations. To mitigate these vibration risks, a nonlinear energy sink (NES) is proposed. First, the finite element analysis method is used to obtain the levitation force data of the superconducting electrodynamic suspension maglev train, and an empirical formula for the resultant force of levitation force and gravity is established by way of fitting. Then, a dynamic model of the train under external force excitation is developed. Based on the harmonic balance method, the approximate analytical solution for the steady-state response of the suspension frame amplitude, suspension frame acceleration, car body amplitude, car body acceleration, additional mass block amplitude, and additional mass block acceleration are derived. The influence of NES parameters on various dynamic indicators are analyzed, and the NES parameters are optimized under the suspension clearance constraint with the objective of minimizing car body acceleration. The study reveals that: as the mass of the additional mass block m3 of the NES increases, the amplitude and acceleration of the suspension frame minimally increase, while those of the car body decrease. As the nonlinear stiffness k3 increases, the amplitude and acceleration of the suspension frame minimally decrease, while those of the car body increase. As the damping c3 increases, the amplitude and acceleration of the suspension frame and car body increase. Particle swarm algorithm is used to obtain the optimized parameters of the NES, leading to the significant improvement in dynamic performance of maglev train compared to pre-optimization results.