This study evaluated the Hook-up installation of an offshore site construction process, which is the final step in an offshore site installation process. During Hook-up installation, the offshore structure can have a detrimental effect on the work stability due to low-frequency motion. Moreover, economic costs can be incurred by the increase in available days of a tugboat. Therefore, this study developed a numerical analysis program to assess the dynamic behavior of mooring systems during hook-up installation to analyze the generally performed installation process and determine when the tugboat should be released. In this program, the behavior of an offshore structure was calculated using Cummin's time-domain motion equation, and the mooring system was calculated by Lumped mass method (LMM). In addition, a tugboat algorithm for hook-up installation was developed to apply the Hook-up procedure. The model used in the calculations was the barge type assuming FPSO (Floating production storage and off-loading) and has a taut mooring system connected to 16 mooring lines. The results of the simulation were verified by comparing with both MOSES, which is a commercial program, and a calculation method for restoring coefficient matrix, which was introduced by Patel and Lynch (1982). Finally, the offset of the structure according to the number of tugboats was calculated using the hook-up simulation, and the significant value was used to represent the calculation result.