Based on the Monte Carlo (MC) method and the fast Fourier transform micromagnetism (FFTM) method, the magnetic dynamic properties of the stacked Co nanoring arrays with different thickness are simulated. It is found that the hysteresis loops of Co nanorings with different thickness have the bistable states, and the formation and stability of the "vortex state" are significantly related to the thickness. Further studies show that the thickness of the stacked Co nanoring arrays has a great influence on the external magnetic field required for the system to reach saturation. The step width of the hysteresis loop ΔH_fc is also related to the thickness. The simulation results are close to the experimental facts.