The forthcoming sixth-generation (6G) mobile networks are envisioned to provide seamless high rate services under the scenario of high user mobility, which cannot be adequately supported by existing mobility management frameworks in the fifth-generation (5G) mobile networks. In this article, to deal with these issues, we investigate mobility management problem in a novel fully-decoupled radio access network (FD-RAN) architecture designed for 6G. Specifically, we first give an in-depth elaboration on the architecture and mechanisms of FD-RAN, explore potential mobility management challenges, and then propose a handover-free mobility management framework tailored for FD-RAN, aiming at providing continuous, satisfactory, and on-demand services for mobile users. Finally, we present a case study where an artificial intelligence (AI)-empowered approach is applied for mobility management in the downlink FD-RAN, and we validate its effectiveness through extensive simulations.