Along the northern margin bounded by the Altyn Tagh Fault, the Tibetan Plateau has been uplifted relative to the Tarim Basin and horizontally extruded to the east for hundreds of kilometres. The Altyn Tagh Fault separates the western Kunlun Shan and Altyn Shan from the Tibetan Plateau, and these two mountain ranges form a topographic window through which river sources from the northern Tibetan Plateau flow into the Tarim Basin. In this study, we designed a specialized geomorphic sandbox to investigate major factors controlling the drainage development on the northern Tibetan Plateau. The modelling results revealed that the Altyn Tagh Fault and preexisting topography played dominant roles in reorganization and divide migration. This strike-slip fault together with the topographic window has controlled the formation and frequent reorganization of two disproportional fault-related drainage basins, with the eastern one much larger than the western one. Large-scale horizontal slip along the fault has resulted in an asymmetric distribution of the drainage area, which showed eastward deviation relative to the topographic window. The modelling results are supported by the observed fluvial landforms as well as evidence of captured channels in nature. Rightward decreasing of the denudation and headward erosion rates in three-step patterns in the model showed that the slip direction of the main plateau relative to the position of the topographic window influences the erosional dynamics. We conclude that the tectonic activity along the Altyn Tagh Fault, together with the preexisting topography, controlled the drainage development and dynamics in the northern Tibetan Plateau in the late Cenozoic.