Natural gas hydrate has been identified as a new alternative energy resource which has characteristics of weak cementation, low reservoir strength and shallow overburden depth. Thus, the stability of subsea equipment and formation can be affected during the drilling process. To quantitative assessment on the vertical displacement of the strata induced by hydrate decomposition and clearly learn the influence laws of various factors on wellhead stability, this study established a fully coupled thermo-hydro-mechanical-chemical (THMC) model by ABAQUS. The important factor that affects the wellhead stability is the decomposition range of hydrate. Based on this, the orthogonal experimental design method was utilized to analyze the influence laws of some factors on wellhead stability, including the thickness of hydrate formation, initial hydrate saturation, overburden depth of hydrate sediment, and mudline temperature. The results revealed that, the decomposition of hydrate weakens the mechanical properties of the hydrate formation, thus leading to the compression of the hydrate formation, further causing the wellhead subsidence. The factors were listed in descending order as follows according to their significance of influences on wellhead stability: the thickness of hydrate formation, initial hydrate saturation, overburden depth of hydrate sediment, and mudline temperature. In particular, the effect of mudline temperature on wellhead stability is negligible. Hence, these findings not only confirm the influence of hydrate decomposition on wellhead stability, but also provide important implications for the drilling of hydrate-bearing strata.