We have commenced a project to develop a beyond-1 GHz solution NMR spectrometer using a HTS coil. Due to a small residual resistance present in the HTS conductor and joint resistance between conductors, a stable persistent current sufficient for NMR measurements is unlikely. Therefore, a current has to be supplied to the HTS coil from an external power supply. The ripple of an external power supply causes a field fluctuation which must be stabilized. In this study we show results of NMR measurements using a 500-600 MHz NMR in such an external current mode: the field fluctuations are stabilized by an internal 2H lock. The field fluctuation from the external power supply comprises a major field fluctuation component at low frequencies, 0.003-0.005 Hz, and superimposed minor field ripples at 2 Hz and 50 Hz. The former limits the time interval of the internal 2H lock, while the latter generates sidebands in the NMR spectrum. Sideband and baseline noise are controlled by appropriate selection of the feedback loop parameters of the lock. The quality of the 1D-solution NMR spectra observed in external current mode is equivalent to that obtained in persistent current mode. However, if the feedback loop time is as short as the gradient pulse width, refocusing of the NMR signal is lost and NMR peaks disappear. The 2D-NOESY and the 2D-HSQC spectra of ubiquitin in an external current mode have been acquired. The quality of the 2D spectra is equivalent to those obtained in persistent current mode; i.e. the internal 2H lock operates stably over an experimental time interval of 40-50 min. To realize a beyond-1 GHz NMR spectrometer, further investigations must be made of (i) the long term stability of a DC power supply, (ii) the enhancement of the compensation field limit for the internal 2H lock, (iii) the extension of the helium refill time interval, and (iv) a method to correct the field homogeneity in the external current mode.