Ensuring the safety of umbilical cables is a core challenge in deep-sea robotics. The umbilical cable usually amplifies the motion amplitude of the mother ship owing to its elastic material. Under the joint action of the mother ship motion and ocean current, the strong internal force waves generated in the umbilical cable tend to cause serious accidents such as umbilical cable breakage. Based on the Kirchhoff rod theory, a dynamic model of an umbilical cable under complex sea conditions is established. The differential quadrature method and Newmark method are used to discretize the equation in the space and time domains. The characteristics of the umbilical cable under different conditions are analyzed. The results show that the amplitude amplification rate of the umbilical cable is directly proportional to the velocity of the ocean current and amplitude of the mother ship motion, and inversely proportional to the period of the mother ship motion. When the length of the umbilical cable changes, the amplitude amplification rate reaches a maximum at 3000 m.