An effective method, involving time and frequency domains was developed to interpret seismic precursors by comparing groundwater-level fluctuations recorded immediately and long before the occurrence of a known earthquake. The proposed method, consisting of the pre-processing (3-point filtering, band-pass filtering, and spectrum analysis) and post-processing (weighted moving average method and histogram and spectrum analyses) stages, was applied to the groundwater-level time series measured at three monitoring wells on Jeju Island, South Korea, from 00:00 on 8 September 2016 to 00:00 on 22 September 2016. The Gyeongju earthquake (Mw 5.4) occurred at 20:32 on 12 September2016. The histogram analysis exhibited an accentuating bellshape as the total number of waveforms, including those caused by the earthquake, of the groundwater-level fluctuations increased. The weighted moving average analysis indicated that various abnormal waveforms with different periods occurred in the fluctuations approaching the occurrence of the earthquake. The periods of seismic precursors in the groundwater-level fluctuations were determined by spectrum analysis and varied among the monitoring wells. Seismic precursor responses attributable to the Gyeongju earthquake were identified at least 8 hours before the earthquake, and the method used in this study indicates its good potential to predict an impending earthquake.