This paper has conducted research on Hook-up installation of offshore site installation process. Hook-up installation is the final step in offshore site installation process, and conducted with AHTS(Anchor Handling Tug Supply vessel) which retrieve the bottom line and tug boat for station keeping. During Hook-up installation, the offshore structure can have a detrimental effect on work stability due to low frequency motion and economic costs can be occurred by increasement of available days of tug boat. This study developed a numerical analysis program for the dynamic behavior of mooring systems during hook-up installation to review the generally performed installation process and determine when the tug boat should be released. In this program, the behavior of offshore structure is calculated by Cummin’s time domain motion equation and the mooring systems are calculated by Lumped Mass Method(LMM). In addition, the program is calculated by tug boat algorithm for hook-up installation. The model used in the calculations is barge type assuming FPSO and has a taut mooring system with 16 moorings connected. The hook-up simulation calculates offset of the structure according to the number of tug boats, and the calculation result is shown using significant value. The hook-up installation procedure was constructed so that the offset of the structure does not exceed 6 m, and the released timing of tug boats was decided considering the stability and economic aspects of the structure.