Orbital angular momentum (OAM) modes of electromagnetic (EM) waves have been extensively studied to obtain more than two independent channels at a single frequency. Thus far, however, multiple radiators have been used to achieve this goal in wireless communications. For the first time, a single radiator was designed to simultaneously transmit three OAM waves in free space at the same frequency. Our design makes use of the radiating resonant modes of a dielectric resonator antenna (DRA). For demonstration, a wireless communication system consisting of a pair of transmitting and receiving OAM DRAs was setup and measured. Three EM waves carrying three different signals were transmitted and received successfully, increasing the system throughput without requiring any complex signal processing algorithms. It confirms that a single radiator can wirelessly transmit more than two independent EM waves at a single frequency by using multi-OAM modes. The work is useful for the future high-speed wireless communication systems.