We propose a novel active fiber design for selectively generating cylindrical vector beams (CVBs) or cylindrical vector modes (CVMs) which can be applied to conventional fiber lasers. A fiber is designed to have a ring-shaped core refractive index profile which can lead to the best overlap between the active dopant distribution profile and the lowest-order CVM (LCVM) field profile. Therefore, the overlap factor (OVF) of the LCVM becomes even higher than that of the fundamental mode. We emphasize that this condition cannot be satisfied by a conventional step-index core fiber (SICF) but by the ring-doped core fiber (RDCF). Because the lasing threshold is inversely proportional to the OVF, the LCVM can predominantly be stimulated even without going through special procedures to impose extra loss mechanisms to the fundamental mode. We numerically verify that the OVF of the LCVM with the doped ions can significantly exceed that of the fundamental mode if the proposed fiber design is applied. In addition, an RDCF of the proposed fiber design can also operate in a regime containing no higher-order modes besides the LCVM, so that it can selectively and efficiently generate the LCVM without being disrupted by the parasitic lasing of the higher-order modes. We highlight that an optimized RDCF can lead to a >30 % higher OVF ratio than a SICF having the same doped area. The proposed model is expected to be useful for enhancing the efficiency of generating CVBs in an all-fiber format.