The 1600-km-long Kunlun Fault striking E-W to WNW-ESE had long been recognized as one of the major left-lateral strike-slip faults bounding the Tibetan Plateau, and ranked one of the most active faults in China continent. During the past hundred years, over twenty strong earthquakes occurred along and near the Kunlun Fault, including six large earthquakes (M > 7). Since some major highly-populated and industrialized cities are close to the Kunlun Fault, understanding of stress transfer and earthquakes migration along the Kunlun Fault is most important for assessing seismic hazard in this region. In this study, by integrating coseismic effect, viscoelastic relaxation and tectonic loading, we studied the evolution of the regional Coulomb stress field by analyzing a sequence of strong earthquakes along the Kunlun Fault. We studied the stress evolution over one century by analysing a sequence of five earthquakes (M ≥ 7) that occurred along the Kunlun Fault since 1937. The model of dislocation sources embedded in a mixed elastic/inelastic layered half-space was used, and the layered model and relevant parameters were constrained by seismic studies. Fault rupture locations and geometry, as well as slip distribution of earthquakes were taken from field observations and seismic studies. Numerical results showed a good correlation between stress transfer, accumulation and earthquakes occurrence. All four studied earthquakes occurred after the 1937 Tuosuo Lake quake were encouraged by the preceding earthquakes with positive stress loading. In subject to the choice of the earthquake source parameter two or three out of four events occurred in regions that experienced previous coseismic and postseismic stress changes of at least 0.01 MPa, suggesting that earthquake triggering due to stress transfer has occurred along the Kunlun Fault. The total stress change since 1937 of the Kunlun Fault region has lead to high levels of stress accumulated on the Xidatan-Dongdatan segment and Maqin-Maqu segment, which have not experienced any significant large earthquake over at least several hundred or several thousand years. The accumulated stress raises the potential earthquake hazard in these areas. Our study demonstrated the crucial importance of postseismic viscoelastic relaxation in the stress transfer and accumulation following large earthquakes.