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The sensitivity of fluvial sediment load to climate change and predictions of future sediment load in cold basins remain poorly investigated, although changes in river sediment transport have important geomorphological, ecological, and societal implications. Here, we adapt a sediment elasticity approach to examine the sensitivity of fluvial suspended sediment load to changes in air temperature and precipitation in the headwater of the Yangtze River (HYR) on the inner Tibetan Plateau. Results show that every 1 °C increase in air temperature can increase the suspended sediment load by 14–27 % by intensifying thermally-driven glacial and permafrost erosional processes, and every 10 % increase in precipitation can increase the suspended sediment load by 16–24 % through enhancing pluvial-driven erosional processes. We predict an increase of 60–85 % in the suspended sediment loads in HYR by 2050 relative to the present-day period under the Representative Concentration Pathway 4.5, as both air temperature and precipitation are projected to increase. Our analysis highlights that smaller upland rivers appear to respond to modern climate change more rapidly and intensively than larger downstream rivers due to the larger glacier and permafrost coverages, poorer vegetation, as well as steeper fluvial relief, and higher sediment connectivity. This study provides a framework and a data-driven sediment elasticity approach to predict climate change and cryosphere degradation-driven changes in future fluvial suspended sediment load in cold basins, highlights the importance of the spatial scale effects in modulating fluvial responses, and has implications for assessing the impacts of climate change on channel morphology and aquatic ecosystems. • A sediment elasticity approach is introduced to estimate sediment load sensitivity to climate change in cold basins • One degree increase in temperature can increase sediment load by 14-27%, and every 10% increase in precipitation can lead to a 16-24% increase in sediment load in HYR • Sediment loads will increase in a warmer and wetter climate, with negative impacts on hydropower and aquatic ecosystems • Sediment loads tend to respond more rapidly and intensively to climate change in upland smaller basins than larger downstream basins [ABSTRACT FROM AUTHOR]