The wind turbine is a high-rise structure, which is subjected to both the vertical loading due to structural weight and the horizontal loading and moment due to blade-induced or tower-induced loading. In designing offshore platforms, it is crucial to evaluate the overall stability and the failure mechanisms of the single-pile composite bucket foundation of the wind turbine under combined loading conditions. Based on the Swipe test loading method and the fixed displacement ratio loading method, this paper investigates the failure envelopes of the single-pile composite bucket foundation on the soft soil ground under undrained conditions in the V-H, V-M, H-M and V-H-M spaces by using the finite element method. It is shown that the failure envelopes in V-H and V-M space are symmetrical, while the failure envelope in H-M space is asymmetrical. Moment load affects the shape of failure envelope in V-H-M space, the failure envelopes of V-H space recedes as the moment load increases. By using the relationship between the actual combined loading and the computed failure envelopes, the stability of single-pile composite bucket foundation can be evaluated in engineering practice.