Floating bodies such as oil rig/production platform and wind turbine in ocean need to be fixed or controlled at expected position by its supporting system which includes tension tendon and catenary mooring-line. Recently, the later one, catenary mooring-line, is increasingly used in deeper water due to its lower cost and easier installment. As the floating platform are developed toward deeper water depth, the length of the mooring-line become larger and consequently the dynamic behaviors such as the structural inertia and hydrodynamic inertia/damping of the mooring-line become more obvious. In this paper, the dynamic behaviors of the mooring-line are considered, and compared with the traditional quasi-static method where only the static restoring force is involved, so as to comprehensively examine the non-linearly restoring performance of catenary mooring-lines. Firstly, the nonlinear dynamic model of the mooring system is developed based on our 3d dynamic catenary equations along with the modified finite element simulations. Compared with the static restoring force, essentially depending on structural gravity and overall shape based on static catenary theory, the dynamic restoring force is analyzed based on our 3d curved flexible beam approach where the structural curvature changes with its spatial position and time in terms of vector equations. In our modified finite element simulations, the rotation degree of freedom between neighboring beam elements is released and bending stiffness of individual element is set to be zero, and the statically original shape and top tension according to the traditional static catenary theory are used as the initial conditions. Moreover, the hydrodynamic force is loaded as depending on structural motion. Based on our numerical simulations, the influences of the amplitude and frequency of the catenary's top-end motion, along with the structural parameters (including the mass density and initial tension ratio), on mooring line's temporal spatial evolution of displacement and dynamic tension are studied. Also, the slack-taut phenomenon caused by structural /hydrodynamic inertia and damping are presented Our results show: 1) Generally, the displacement distribution along the mooring-line is characterized as a stable stand wave. The additional part of restoring tension due to the dynamic effects is up to 20% of the quasi-static method, and the tension amplitude difference (between the maximum tension and minimum tension) is around three times of the quasi-static value. Particularly, as the mooring-line becomes slack, the response is characterized as travelling wave, the maximum tension amplitude is up to 9 times of the static method. 2) As the amplitude/frequency of the catenary 's top-end motion increases, the value of catenary displacement firstly drops and then rises. The displacement distribution along catenary length changes with the motion of top end. Interestingly, the maximum displacements occur at the middle point of the catenary for case of surge while the maximum displacement moves up along the catenary as the top end motion gets larger for case of heave. 3) The magnification factor of top tension drops with increase of mooring-line mass density but rises with the increase of the initial tension ratio. It is also noted the velocity amplitude at higher frequency in the velocity spectrum may increase as the top end motion increases.