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. The properties of HTS appear to cause poor magnetic field stability in the persistent-mode operation. Therefore, in this study, a high-field NMR magnet including HTS coils will be operated in the driven-mode. In order to evaluate the magnetic field stability in the driven-mode, we modified a 14 Tesla (600 MHz) vertical NMR magnet. With regard to the magnet, persistent switches for axial shim coils (z0, Z1, Z2) as well as the main coil were removed for constant operation with a power supply. In addition, a 1 W Gifford-McMahon (GM) cryocooler at 4 K and HTS current leads were installed in the cryostat to re-condense boiled helium gas. As a result, there was a long-term change of about 6 ppm in the magnetic field stability, but, in the short-term (a few hours), a change of about 2 ppm was observed. By the z0 shim control, in combination with the NMR field measurement, an averaged magnetic field drift of less than 0.0001 ppm/h was achieved.