Natural gas hydrate reservoir 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 quantitatively assess the vertical displacement of the formation induced by hydrate decomposition and clearly identify the influence laws of various factors on wellhead stability, this study established a fully coupled thermo-hydro-mechanical-chemical (THMC) model by using ABAQUS software. The important factor that affects the wellhead stability is the decomposition range of hydrates. 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. When the duration of drilling operations was 24 h and no decomposition of natural gas hydrate occurs, the wellhead subsidence is recorded at 0.053 m, this value increases with an increase in drilling fluid temperature. The factors were listed in descending order as following, 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. Among the above factors, statistical significance of the mudline temperature was less than 15% confidence level, suggesting that the effect of mudline temperature on wellhead stability is negligible. These findings not only confirm the influence of hydrate decomposition on wellhead stability, but also suggest important implications for the drilling of hydrate-bearing formation.