With Monte Carlo simulation,we study magnetic properties and controllable vortex circulation of asymmetric Co nanorings.Simulated results indicate that magnetic field direction has great effect on magnetic states and magnetization process of asymmetric Co nanorings.It is found that direction of the magnetic-moment circulation in asymmetric nanorings can be controlled by gradient of the domain-wall energy along the circumference in cooperation with an external magnetic field.It is found that size effect is obvious on stability of vortex-type state and magnetization process of asymmetric nanorings.