Abstract The changing tides have always attracted the attention of oceanographers. Current nonstationary analysis methods are widely employed in tides, but they still have their own limitations. Based on the classical harmonic analysis and Fourier series, an extended harmonic analysis method, F_TIDE, is developed to deal with the nonstationary tidal signals. The efficiency of F_TIDE and the credibility of results with data gaps are validated by analyzing prescribed sea levels in the ideal experiments. The time-vary amplitudes and mean sea levels (MSLs) captured by F_TIDE are consistent with those obtained by T_TIDE through analyzing hourly sea level observations from two gauges at Nome (Alaska) and South Beach (Oregon). Near the two endpoints of the analyzed time series, the hindcast of F_TIDE is more accurate than S_TIDE that is a powerful nonstationary tidal analysis tool.