The warming climate has posed a serious threat on ground surface stability. In permafrost regions, ground surface instability may induce engineering and geological disasters, especially for the engineering corridor. It is difficult to evaluate ground surface stability over permafrost because the stability is influenced by various factors in permafrost regions. Many single index models cannot comprehensively evaluate the ground surface stability for permafrost. We, therefore, proposed an evaluation model considering different influential factors based on the trapezoidal fuzzy Analytical Hierarchy Process (AHP) method. And the ground surface stability was calculated and analyzed along the Qinghai–Tibet Engineering Corridor under three climate warming conditions (the slow climate warming, the medium climate warming and the rapid climate warming). The results show that the ground surface stability influential factors, including the mean annual ground temperature, the active layer thickness, and the volume ice content, will be greatly changed with the warming climate. By 2100, the percentage of high-temperature permafrost (−0.5 °C < T ≤ 0 °C) will increase about 29.45% with rapid climate warming. The active layer thickness will have an average thickening rate of about 0.030 m/year. Most of the high ice content permafrost will change to low ice content permafrost. The ground surface stability, therefore, will be greatly changed with the warming climate along the Qinghai–Tibet Engineering Corridor. Compared to the present, the stable area will decrease about 5.28% by 2050 under the slow climate warming. And that is approximately 7.91% and 21.78% under the medium and rapid climate warming, respectively. While in year 2100, the decrement is obviously increased. The stable area will decrease about 11.22% under the slow climate warming and about 17.3% under the medium climate warming. The proportion of stable area, however, has an increasing trend under the rapid climate warming. This phenomenon is mainly caused by the warming climate which can lead to the permafrost being degraded to melting soil. The unstable area is mainly distributed near the Chumaer River high plain, Tuotuohe–Yanshiping, Wudaoliang, Tangula Mountains, and other high-temperature permafrost areas. This paper provides a reference for geological hazard prevention and engineering construction along the Qinghai–Tibet Engineering Corridor.