A 20 T/ϕ32 mm all REBa2Cu3O7−δ (REBCO, RE = rare earth) REBCO superconducting magnet for 850 MHz nuclear magnetic resonance spectroscopy is being designed. The high-temperature superconductors, REBCO-coated conductors with both high tensile stress and high critical current density under high magnetic field would allow superconducting magnets to be compact and lighter than their low-temperature superconductor counterparts. The 20-T REBCO superconducting magnet consists of a stack of 28 double-pancake coils with the so-called no-insulation methods. Considering the perpendicular magnetic field to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -axis, five different width tapes, i.e., 4.1, 5.1, 6.1, 7.1, and 8.1 mm were placed on the midplane to both end positions in an axial direction. To improve the magnetic field homogeneity, the inside notch on the 4.1-mm tapes was adopted. The peak-to-peak magnetic field homogeneity over a 5-mm diameter spherical volume is better than 0.8 ppm. In this article, the design of the REBCO coils, electromagnetic field analysis, and stress analysis of the superconducting coils were presented.