Systems of ocean current power generation are generally moored deep in the seabed. The mooring system is like ropes. The ropes are very long and can provide tension but not compression, and their dynamic displacement is large and unstable, which is different from traditional structures. To generate high-efficiency ocean current power generation, it is necessary to design a stable mooring system. Maintaining the stability and small dynamic displacement of the ocean current invertor is significantly helpful for the high efficiency of the invertor. In addition, the stability of the mooring system and a small dynamic tension, high safety factor, and long life of the mooring ropes are essential. In this study, we investigate the transient behavior of a mooring system composed of an inverter platform, pontoon, and ropes under initial conditions. An analytical method is proposed. The transient translational and rotational displacements are composed of 36 independent normalized fundamental solutions. The composition depends on the initial conditions. Each fundamental solution is derived by using the Frobenius method. This study proposes the replacement of the traditional single-rope mode with the double-rope parallel mode, which can maintain a high fracture strength and low effective spring constant in the rope. It is verified that this design can decrease instantaneous tension and increase the safety factor of the rope. Additionally, high hydrodynamic damping coefficients can significantly increase the stability of the mooring system.