Due to the special rectangular cross section of the REBCO tapes, the screening current-Induced magnetic field (SCIF) in a REBCO high temperature superconducting (HTS) coil will deteriorate the spatial homogeneity and temporal stability of the superconducting magnet, which is a key issue for the application of HTS magnets in the Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI) devices. In this paper, a method, through a small size radio frequency antenna (RFA) located inside/outside of the REBCO HTS non-insulation coils, was proposed to eliminate the SCIF generated in the REBCO coils. By controlling the eddy current loss generated in the HTS coil, the temperature distributions will be affected, which has an effect on the critical current distributions in the REBCO HTS coil. This will lead to a re-distribution of screening current in the REBCO HTS tape. In the paper, the effects of shape, working conditions, and relative position of RAF on the elimination of SCIF was studied and investigated. An improved numerical method was used to simulate the SCIF in the HTS magnet and the efficiency of the RAF. And also, the related experiments were performed at 77 K and compared with the simulation results, which shows a good agreement. These results will help us design and fabricate a 15 T non-insulated HTS insert for the 30 T all-superconducting magnet in the near future.