The development of a dry-tree semisubmersible (DTS), a new type offshore hydrocarbon production system, is facing unconventional challenges in the issues of dynamic stability, structural integrity, and parametric resonance. Mathieu equation is utilized to assess the dynamic stability of a top-tensioned riser (TTR) in order to prevent the parametric resonance which leads to detrimental effects on the structural integrity. The objectives of this paper are (i) to study a Mathieu stability diagram and its coefficients for an assessment of the stability of a TTR; (ii) to identify the effects of the dynamic tension variations in the Mathieu stability assessment; (iii) to analyze the stability of the TTR on a DTS, which is equipped with a long stroke tensioner, by using a numerical simulation. The dynamic tension variation in the DTS was identified to induce instability in the TTR. Hence, the Mathieu stability assessment is recommended to be included in an analysis of TTR behaviors in a dry-tree interface of semisubmersibles.