The taut mooring system using polyester rope as the mooring lines overcomes the heavy weight of the traditional chain mooring material and provides better mooring performance for the floating structures, which attracts much attention in the field of deep-water mooring. The nonlinear mechanical properties of the polyester make it more difficult to predict the tension response of the material. Therefore, it is essential to model this nonlinear relationship accurately. In this paper, based on the absolute nodal coordinate formulation under the condition of large axial tension and combined with the dynamic stiffness model of 8-strand braided polyester rope, the tension response of the polyester line is accurately calculated and analyzed, and the results are compared with the approximate method. The simulation shows that the axial tension of the polyester cable obtained by the accurate model is larger than that of the approximate method. The nonlinear constitutive relationship of the polyester cable displays the phenomenon that the larger stretch, the larger sitffness is. Besides, the approximate method will distort the tension prediction. Therefore, it is necessary to adopt an accurate dynamic stiffness model in calculating the tension response of mooring systems using polyester material.