In order to simulate the dynamic behavior of tether cables in tethered system, a new ANCF cable element was proposed by using the absolute nodal coordinate formulation (ANCF). The number of layers of cables and the mechanical properties of materials in each layer all were considered in the element. The Kelvin-Voigt model was used to explain the viscoelastic properties of the inner core layer, and the improved Yeoh model was applied to the sheath layer to explain the hyperelastic properties of materials. Moreover, a difference scheme with implicit effect was designed to solve the dynamic differential equation numerically. Finally, the accuracy and convergence of element were proved by a series of static and dynamic numerical calculations, and the ANCF elements using several different hyperelastic materials were compared, which proved the rationality and superiority of the ANCF cable element using the improved Yeoh model.