Due to its very high critical fields, the second-generation high-temperature superconductor (2 G HTS) has been, and is being, used in high-field magnets. However, a persistent screening current induced in the REBCO conductor under time-varying conditions distorts the magnetic field, spatially and temporally. We describe a novel REBCO conductor design composed of narrow-stacked (NS) wire, a bundle of 1 mm wide REBCO tapes. The design is based on a fundamental notion that the narrower the REBCO tape width, the smaller the screen-current field (SCF). In this paper, both experimental and simulation work were carried out to analyze SCF in a REBCO coil wound with an NS wire. We demonstrate that the critical current of NS wires can be consistent with the conventional REBCO tape to meet the application requirements. Meanwhile, NS wire indeed substantially results in small SCF, an important requirement in high-field magnets such as for NMR, MRI, and HEP that may rely on REBCO conductor.