REBCO coated conductors having a performance greater than 300 A/cm at 77 K have been developed for superconducting applications. The conduction-cooled coils fabricated using REBCO coated conductors are expected to have the high performance because the specific heats of the constituent materials increases greatly with the operating temperature. From the point of view of the coil design using REBCO coated conductors, we must consider the critical current versus the magnetic field characteristics and their temperature dependence. In this study, we fabricated the two-layer stacked racetrack coil whose outer diameter was 92 x 172 mm with 56 turns. The coil used the REBCO coated conductor, whose critical current was around 200 A/5 mm at 77 K self field, manufactured by Fujikura Ltd. We compared with the calculated and measured the voltage distribution of one racetrack coil, which was attached with voltage taps each turn, at 77 K in self field. We investigated the I-c of the two-layer coil at 65 K and 50 K under conduction-cooled conditions. The I-c values of the two-layer coil in self field using a criterion of 10(-7) V/cm were achieved 220 A at 65 K and 386 A at 50 K, which the central magnetic fields were 0.13 T at 65 K and 0.23 T at 50 K, respectively. (C) 2012 Published by Elsevier B.V.