We have shown that a persistent current can be induced in HTS coils with the form of double pancakes or single solenoids by the technique of joint-less winding with 2G REBCO tapes. However, the inevitable gap located at the center of the joint-less coil caused very poor magnetic field homogeneity, which was shown by the magnetic field mapping from the previous experimental work. In this paper, to improve the performance of the coil, we proposed another HTS coil wound by the same joint-less technology but arranged differently. A conventional joint-less coil usually has two coil parts arranged coaxially, but the proposed one will have two coil parts arranged concentrically. By this arrangement, we could improve the magnetic field homogeneity by removing the unfavorable gap near the magnet center. We tried to induce the persistent current in the fabricated coil system in the operating temperature of 20 K reached by the conducting cooling system with a GM cryocooler. After maintaining the persistent current mode for 15 hours, we carried out the magnetic field mapping to analyze the harmonics of the central field under the 10-mm DSV. The analyses data will be used for the future design work of the passive shimming.