We determine the finite-fault slip distribution of the 2001 Kunlun earthquake (Ms = 8.1) by inverting teleseismic waveforms, as constrained by geological and remote sensing field observations. The spatial slip distribution along the 400-km-long fault was divided into five segments in accordance with geological observations. Forward modelling of regional surface waves was performed to estimate the variation of the speed of rupture propagation during faulting. For our modelling, the regional 1-D velocity structure was carefully constructed for each of six regional seismic stations using three events with magnitudes of 5.1-5.4 distributed along the ruptured portion of the Kunlun fault. Our result shows that the average rupture velocity is about 3.6 km s-1, consistent with teleseismic long period wave modelling. The initial rupture was almost purely strike-slip with a rupture velocity of 1.9 km s-1, increasing to 3.5 km s-1 in the second fault segment, and reaching a rupture velocity of about 6 km s-1 in the third segment and the fourth segment, where the maximum surface offset, with a broad fault zone, was observed. The rupture velocity decelerated to a value of 3.3 km s-1 in the fifth and final segment. Coseismic slip on the fault was concentrated between the surface and a depth of about 10 km. We infer that significant variations in rupture velocity and the observed fault segmentation are indicative of variations in strength along the interface of the Kunlun fault, as well as variations in fault geometry.