This study established the conditions in which mooring load is minimized in a fish cage that includes a damping buoy in specific wave conditions. To derive these conditions, numerical simulations of various mooring contexts were conducted on a fish cage (1/15 scale) using a simplified mass-spring model and fifth-order Stokes wave theory. The simulation conditions were as follows: (1) bridle-line length of 0.8–3.2 m; (2) buoyancy of 2.894–20.513 N for the damping buoy; and (3) mooring-rope thickness of 0.002–0.004 m. The wave conditions were 0.333 m in height and 1.291–2.324 s of arrival period. Consequently, the mooring tensions tended to decrease with decreasing mooring line thickness and increasing bridle-line length and buoyancy of the buoy. Accordingly, it was assumed to be advantageous to minimize the mooring tension by designing a thin mooring line and long bridle line and for the buoyancy of the buoy to be as large as possible. This approach shows a valuable technique because it can contribute to the improvement of the mooring stability of the fish cage by establishing a method that can be used to minimize the load on the mooring line.