Based on Monte Carlo simulation and fast Fourier transformation and micromagnetism (FFTM) method, magnetic properties of cobalt (Co) nanorings with different asymmetry have been studied. Spin configurations, magnetization hysteresis loops, as well as remanence of the Co nanoring systems with different asymmetry were calculated to demonstrate the difference in magnetization dynamics processes. The calculated results indicate that asymmetry has an important effect on magnetic properties of the asymmetric Co nanorings. It is found that with decreasing asymmetry the hysteresis loops of asymmetric Co nanorings drop and form new step, and then form multi-steps or double-step, which can be explained as the change of spin configurations. The remanence of the systems decline in the twists and turns, which shows a local minimum as a = b, and at the same time, the remanence with [Formula: see text] periodically changes. Spin configurations and shape of the system account for these results.