Based on digital teleseismic P-wave seismograms recorded by 28 long-period seismograph stations of the global seismic network, source process of the November 14, 2001 western Kunlun Mountain MS=8.1 (MW=7.8) earthquake is estimated by a new inversion method. The result shows that the earthquake is a very complex rupture event. The source rupture initiated at the hypocenter (35.95°N, 90.54°E, focal depth 10 km, by USGS NEIC), and propagated to the west at first. Then, in several minutes to a hundred minutes and over a large spatial range, several rupture growth points emerged in succession at the eastern end and in the central part of the finite fault. And then the source rupture propagated from these rupture growth points successively and, finally, stopped in the area within 50 km to the east of the centroid position (35.80°N, 92.91°E, focal depth 15 km, by Harvard CMT). The entire rupture lasted for 142 s, and the source process could be roughly separated into three stages: The first stage started at the 0 s and ended at the 52 s, lasting for 52 s and releasing approximately 24.4% of the total moment; The second stage started at the 55 s and ended at the 113 s, lasting for 58 s and releasing approximately 56.5% of the total moment; The third stage started at the 122 s and ended at the 142 s, lasting for 20 s and releasing approximately 19.1% of the total moment. The length of the ruptured fault plane is about 490 km. The maximum width of the ruptured fault plane is about 45 km. The rupture mainly occurred within 30 km in depth under the surface of the Earth. The average static slip in the underground rocky crust is about 1.2 m with the maximum static slip 3.6 m. The average static stress drop is about 5 MPa with the maximum static stress drop 18 MPa. The maximum static slip and the maximum stress drop occurred in an area within 50 km to the east of the centroid position.