In this paper, we introduce a new type of controllable auto-focusing vortex beam array named annular quasi-Airy vortex beam array (QAVBA), which can reduce the crosstalk among different orbital angular momentum (OAM) modes of optical vortex. The effects of initial beam parameters of annular QAVBA and propagation conditions on the OAM mode propagation performance are investigated. The results indicate that the topological angle θ, the topological charge m, and the decay parameter α could manipulate the auto-focusing characteristics of annular QAVBA and regulate the crosstalk of OAM modes. The crosstalk among OAM modes increases with the turbulence strength. Interestingly, the annular QAVBA with obtuse topological angle is favorable for the OAM mode transmitting at far propagation distance or in strong atmospheric turbulence when the decay parameter α is large enough for the energy of annular QAVBA mainly concentrating on the main light ring. Our research provides a reference for optimizing the design of light sources and free-space optical communication system with annular QAVBA.