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. The Mathieu equation is used to assess the dynamic stability of a top-tensioned riser (TTR) in order to prevent the parametric resonance which leads to detrimental effects on structural integrity. The objectives of this paper are to (i) study a Mathieu stability diagram and its coefficients for an assessment of the stability of a TTR, (ii) identify the effects of the dynamic tension variations in the Mathieu stability assessment, and (iii) analyze the stability of the TTR on a DTS, which is equipped with a long-stroke tensioner, by using 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.