The circular phased array is one of the main methods to generate radio frequency orbital angular momentum (RF-OAM) beams with high purity and capability of OAM-beams steering, but OAM beams generation and steering are only related to angle, not range dimensions. Therefore, the mode of OAM beams can be easily received in a wide range and intercepted by unintended eavesdroppers in the beam axis. As a promising solution, a range-angle dependent OAM beams transmission scheme is highlighted by the frequency diverse array (FDA) for the sake of the OAM secure transmission in this paper. In order to realize the range-angle dependent OAM beams, a special frequency interval between adjacent antenna elements in the FDA is designed and illustrated. The modes of OAM beams generated by the FDA can only be observed in the legal target location. Numerical results show that the scheme can effectively realize the safe transmission of OAM beams, i.e., reducing the possibility of the OAM beams being tapped, improving the OAM-beams transmission performance, and enhancing the energy efficiency with low complexity.INDEX TERMS Orbital angular momentum (OAM), frequency diverse array (FDA), secure transmission.