A study of the 14 November 2001 Kokoxili earthquake is performed to estimate the source parameters from teleseismic body-wave inversion. The earthquake broke the western Kusai Hu segment of the east–west trending Kunlun strike- slip fault, with the presence of surface rupture traces over 400 km. This event of Mw 7.8 (Harvard CMT, 2001) was followed by moderate but continuous seismic activity. We apply an inversion method of complex body waves with multiple subevents (Kikuchi and Kanamori, 1991) to model the waveforms and to understand the rupture process. Field observations are used to constrain the inversion and to evaluate the solution. Considering the western complexities of the Kusai Hu segment, we invert the first part of the data to model the initiation of the rupture. The rupture is found to begin on the fault branch lying southwest of the Buka Daban Peak. Although the rupture propagates dominantly eastward, some subevents systematically appear to the west of the epicenter. Then, an inversion of the complete body-wave traces shows that the rupture propagated unilaterally eastward along the straight part of the Kusai Hu segment.