Design, fabrication, and test results of a type persistent-mode high-temperature superconductor (HTS) shim coil are presented. A prototype Z1 rectangle-loop shim, cut from 46-mm wide Y-Ba-Cu-O tape manufactured by AMSC, was fabricated and tested at 77 K. The HTS shim, much thinner than the conventional NbTi shim, is placed inside the main magnet and immune to its diamagnetic wall effects. Combined with the >12-T and >10-K operation capability, the HTS shim offers a versatile design option for nuclear magnetic resonance (NMR) magnets, liquid-helium-free as well as conventional, and is particularly attractive in the next generation NMR magnets. For the NMR (nuclear magnetic resonance) superconducting magnet, its field over a target space where a specimen (the object of spectroscopy) is placed must be very homogeneous. For a high-resolution NMR magnet, this inhomogeneity can be as severe as 0.01 ppm over a 30-mm diameter spherical volume (DSV). The "raw" field of most superconducting magnets is not good enough for NMR spectroscopy and therefore it must be shimmed to a homogeneous field over the specimen volume. [1][2][3] Generally, the superconducting NMR magnet is equipped with its own set of superconducting shim coils ("shims"), currently all wound with NbTi, a low-temperature superconductor (LTS). Because of their field limitations (<12 T even at 1.8 K) and size (typically 15-30 mm radial build), NbTi shims have always been located outside the magnet assembly, i.e., radially furthest away from the magnet center where the sample is placed. This is chiefly because no superconducting shims suitable for the high-field center region have been available. Here, we describe the design concept of the high-temperature superconductor (HTS) shims and results of a prototype Z1 shim, built and operated.For a shim placed outside the magnet assembly, there are two inherent technical disadvantages: (1) at a great distance it must work harder to generate a required shimming field, i.e., a greater ampere (current)-turns (coil size); and (2) its field is attenuated by the "diamagnetic" walls of the magnet assembly, comprising many superconducting coils, as it reaches the magnet center. Worse, this field attenuation is asymmetric to the center and has strong hysteresis.Diamagnetic effect is the manifestation of a screening current induced by a field impinging on a "Bean" cylinder. 1,4-10 We may thus consider a superconducting coil as a Bean cylinder of a diamagnetic wall D thick. 4 Although D cannot be equated directly to the size of a superconductor strand, typically $50 lm for LTS and millimeters for HTS, LTS coils generally have much less attenuating and distorting effects of the diamagnetic wall than HTS coils. However, a sheer size of LTS in a typical all-LTS NMR magnet makes diamagnetic effects in LTS magnets not negligible.In this paper, we describe a design concept for superconducting shims prepared from a "wide" tape of coated YBCO HTS. 11,12 The HTS shim can operate even in a >12-T field and above liquid helium (LHe) tempe...