This paper presents a new method to realize the controllable modes conversion by an anisotropic and slowly rotating potential well. In such potential well, the orbital angular momentum of the beam is not conserved, but exhibits a periodic variation as the propagation distances. Then the modes conversion can occur among the Laguerre-Gaussian, Hermite-Gaussian, and Hermite-Laguerre-Gaussian modes. More interesting, the rotation of the potential well can influence the evolution of OAM and then adjust the mode conversion. When the anisotropic potential well becomes isotropic at certain distance, the various mode solitons which with different rotating velocities and directions can be generated. Furthermore, we also find that the mode of some other more complex beams also can be controlled by the rotation of potential well. Our results provide an excellent opportunity for solitons conversion and generation, optical information processing, and other applications.