This study identified the interrelated elements of multidimensional subsystems such as water resources, energy, and socio-economic factors, environment, and constructed a system dynamic model of the water-energy coupling system in the nine provinces, and autonomous regions of the Yellow River Basin. Driven by the climate scenario of the Shared Socioeconomic Pathway(SSP) provided by CMIP6, the indicators such as Hurst exponent, orderliness, and coupling degree were used to reveal the evolution law of the water energy coupling system in the nine provinces and autonomous regions of the Yellow River Basin under changing climate conditions. The results show that the evolution process of the water energy coupling system in the nine provinces and autonomous regions of the Yellow River Basin can be divided into stages such as development, antagonism, depression, and recovery. Among them, the climate sensitivity of the water resources subsystem is higher than that of the energy subsystem. The water consumption of the primary industry and the energy consumption of the secondary industry are significantly affected by feedback, while the water consumption and energy consumption of the tertiary industry have a strong synergistic evolution characteristic. SSP5 8.5 scenario has the fastest evolution efficiency and highest sensitivity, followed by SSP3 7.0 scenario, and SSP1 2.6 scenario has the slowest evolution efficiency. The Hurst index of the water resources and energy subsystems in the nine provinces and autonomous regions of the Yellow River Basin is relatively high, among which the Hurst index of variables such as water consumption and energy consumption per unit of GDP in the secondary industry is the highest, showing chaotic and disorderly characteristics. The energy subsystem has the highest degree of orderliness, the environmental subsystem has the lowest degree of orderliness, and the information entropy ratio of the energy consumption of the secondary industry and its unit GDP energy consumption is the highest. The random evolution characteristics of each variable are most prominent under the SSP5-8.5 scenario, and the orderliness is highest under the SSP1-2.6 scenario. The coupling degree of water energy systems in the nine provinces and autonomous regions of the Yellow River Basin increased significantly before 2020, but remained in a state of imbalance, and after 2020, it was in a state of basic coordination. The coupling degree is highest under the SSP1-2.6 scenario, indicating that the intensity of basin resource development and increased environmental awareness will enhance system compactness, while an increase in carbon emissions will weaken system stability and coupling.