On November 14, 2001, the M(S)8.1 west of Kunlun pass earthquake occurred in the East Kunlun fault zone of the Qinghai-Xizang Plateau. The results of the field investigation and the rupture process inversion show that this earthquake is a strike-slip earthquake event with a very complex rupture process. Studying the spontaneous rupture process of this earthquake is significant for understanding the mechanism of great continental earthquakes. In this paper, the dynamic rupture process of the 2001 M(S)8.1 west of Kunlun pass earthquake is investigated by using the curved grid finite -difference method (CG-FDM). First, a 3-D non-planar fault model is established, which can represent the main characteristics of the earthquake fault. Constrained by the geological survey, and the inversion results from GPS and InSAR observation data, as well as far-field seismic records, the main characteristics of the earthquake rupture process are reconstructed by the numerical simulation. Then, the influence of background stress field, fault geometry, and frictional coefficient on the fault plane slip distribution, source time function, and rupture propagation velocity are discussed in more detail. The results show that, the clockwise rotation characteristics of the maximum horizontal principal compressive stress along the eastern direction in the Qinghai-Xizang Plateau and the low dynamic friction coefficient on the fault plane may be two important reasons that the M(S)8.1 west of Kunlun pass earthquake developed into a large earthquake with an ultra-long rupture scale. And the dynamic friction coefficient along the fault plane of this earthquake may be non-uniform, resulting in a complex stress drop along the fault strike, which leads to the occurrence of super-shear rupture and controls the distribution of slip on the fault plane.