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The upper reaches of the Yellow River (URYR) comprise the main water-producing zone of the Yellow River Basin. Quantifying the contribution rates of climate change and human activities (CCHAs) to the changes in runoff in the URYR is critical for formulating rational water resource management strategies in the entire basin. The main objective of this study is to combine the advantages of flexible sample entropy and multiscale entropy to propose a new three-stage method (TSM) to quantify the contribution rates of CCHAs to changes in runoff in the URYR above the city of Lanzhou during 1956–2015. The results show that climate change is the dominant factor affecting the changes in runoff in the study area over the period of study. However, compared with the baseline period (BP; 1956–1986), the variation period (VP; 1987–2015) experienced notably different impacts of CCHAs on the runoff changes. Human activities constituted the dominant factor impacting the changes in runoff in the Huangshui River and the lower section of the URYR (average contribution rate of 70.9%). Meanwhile, climate change was the dominant factor affecting changes in runoff in other regions of the URYR (average contribution rate of 91.8%). Declining precipitation, increasing temperature and evaporation, changing watershed surfaces, the construction of reservoirs and water diversion projects, and increasing human water consumption have resulted in varying degrees of runoff complexity. The novelty and uniqueness of this study can be ascribed to the TSM that (1) considers the impacts of human activities on changes in runoff during the BP and combines the advantages of single time-scale and multiscale entropy for the first time; and (2) uses positive and negative contribution rates to represent the increase and decrease in runoff complexity, respectively. The method exhibits appreciable performance and applicability in the URYR and other watersheds to effectively calculate the contribution rates of the CCHAs to changes in runoff. Image 1 • A new complexity-based three-stage method (TSM) was proposed to quantify impacts of climate change and human activities (HAs) on runoff changes (RCs). • The TSM considers the impact of HAs on RCs during the baseline period (1956–1986). • The TSM uses positive/negative contribution rate (CR) to represent runoff complexity increase/decrease. • HAs are the dominant factor influencing RCs, with a 70.9% CR in the lower section of the upper Yellow River. • The TSM performs well and is applicable to this study and other areas. [ABSTRACT FROM AUTHOR]