This paper presents a numerical model of top tension risers (TTRs) with hydro-pneumatic tensioner for Spar application in the Gulf of Mexico environment. Nonlinearity of the stiffness and friction characteristics of the tensioner combined with stick-slip behavior of riser keel joint is investigated. The relationship between tensions and strokes for hydro-pneumatic tensioner is based on the ideal gas equation where the isotropic gas constant can be varied to achieve an optimum stroke design based on tensioner stiffness. Challenges of modeling the coupling effects in the finite element (FE) method between the tensioner and hull motion are also presented. This new FE model is implemented into CHARM3D, a fully coupled time domain analysis program of floating bodies. The effect of nonlinearity of tensioner curve, tensioner friction and riser keel friction is intensively investigated. The resultant global motion, TTR stroke and tensions are systematically compared with those of a simple engineering approach in which the nonlinear coupling effect is captured by linearization.