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Although high-temperature superconductors (HTS) are very promising for high-field generation over 25 T, it is difficult to apply them to an NMR magnet because of their low index values and the difficulty caused by superconducting joints. We have developed a drift compensation technique to apply HTS to a high-resolution NMR using a 14 T (600 MHz) vertical NMR magnet. The magnet had a poor magnetic field stability of about -0.7 ppm/hour, so a drift compensation unit based upon a flux pump method was added. The unit consisted of nested inner (secondary) and outer (primary) coils. The inner coil was connected in series to the main coil circuits, and the outer coil was connected to the auxiliary power supply to sweep the output current very slowly. While the current of the outer coil was changed at an adequate sweep rate by the power supply, the current was induced by inductive coupling in the inner coil. The induced current canceled out the decay of the main coil current that caused the poor drift of the magnet. With the drift compensation unit, the magnetic field drift was improved to less than 0.0001 ppm/hour for 3 days at 14 T. This period was long enough for one NMR measurement.