The large amplitude motion of floating structures could cause slack-taut transformation in the taut mooring system, which may result in snap load. The dynamic finite element analysis model is established to simulate the slack-taut process through adding a series of sinusoidal excitation with different amplitudes and frequencies to the upper end of a taut mooring line. During the slack-taut process, the minimum dynamic tension could be close to zero, and the maximum dynamic tension could come up to several times of pretension. The change laws of dynamic tension during the slack-taut process are compared and summarized. The calculation results show that the phenomenon of slack-taut could occur when the amplitude and frequency of excitation reach some certain value. The mooring line tension spectra show that the doubling and higher frequency components appear in addition to the frequency of excitation. The results could provide a reference for further investigating on the mechanism of snap load and the design of mooring system.