Orbital angular momentum (OAM) provides an additional degree of freedom for information transmission. However, wireless transmissions with OAM are challenged by secrecy issues since the OAM modes can be observed over a wide range along the beam axis, and it allows that the eavesdroppers intercept the information bits encoded on the OAM modes. In this letter, targeting against unintended receivers, we propose a secure range-dependent transmission scheme with OAM radio beams generated by the frequency diverse array (FDA). Specifically, we consider a line-of-sight communication link overheard by an unknown eavesdropper. The transmitter employs FDA of antennas to generate range-dependent OAM radio beams and target at the legitimate receiver, in which the confidential information is encoded on the OAM modes. The eavesdropper outside the target region observes distorted OAM modes and thus is unable to recover the secret messages. The proposed scheme enhances the security of OAM mode modulation and achieves higher energy efficiency compared to the conventional secure transmission schemes with artificial noise.