Aimed at the problem that the coexistent attractors with different topological properties remain in the nonlinear energy sink (NES) system caused by the multi value character, a nonlinear vibration reduction strategy based on the attractor migration control method is proposed. Firstly, the influence of excitation force amplitude on the global behavior of the NES system in the large parameter range is analyzed. Secondly, an improved parallelized multidegreesoffreedom cell mapping (PMDCM) method is proposed to study the coexistent attractors and their basins under typical parameters. Finally, the attractor transitions with different amplitudes are realized by means of migration control. The simulation results show that the NES system in several typical parameter range presents multistable coexistent attractors phenomenon, the PMDCM method has higher efficiency and precision, and the NES system can be migrated from large amplitude attractors to small amplitude attractors by using open plus nonlinear closed loop (OPNCL), reducing vibration and noise.