Based on the three dimensional potential flow theory, three kinds of velocity potentials such as the fluid incident potential, radiation potential and diffraction potential are analyzed through the boundary conditions and control equations, and the catenary method and concentrated mass method are introduced to establish the barge cable coupling motion model for the three stages of the floating installation ship entering, floating installation ship exiting and barge in place and berthing. When the wave direction is 270°, the maximum mooring line tension reaches 176.67 t during the barge in place and berthing stage, and the corresponding mooring line is the port tail. At this time, the safety factor is the minimum of 2.16, and the design tension of the mooring line is 185.20 t. The tension of the tail mooring line decreases in three stages, while the tension of the middle and head mooring lines increases in three stages. The tension errors of the mooring line for ship entering and exiting are 2.3% and 5.6%, respectively obtained by concentrated mass method and MOSES software. The research and design of the mooring motion calculation model for floating barge installation is applicable to the mooring line tension under different working conditions.