One indication of the impacts of climate change on the water cycle is growing streamflow uncertainty, which is especially evident in high and cold regions. An interval forecasting model is established, which couples a snowmelt module and an uncertainty module, based on the Xinanjiang model. The model can consider the climate change impacts by quantifying the streamflow variations in the form of interval forecasts. The model’s performance was assessed by applying it in the headwater region of the Yellow River Basin. Interval forecasts and uncertainty analyses were conducted. Results show that the model can accurately describe the daily streamflow process in the study area. Unlike the deterministic forecasting model, the interval forecasting model effectively addresses shortcomings in forecasting high-flow scenarios. Furthermore, outcomes from the uncertainty analysis indicate that the model parameter K (the ratio of potential evapotranspiration to pan evaporation) plays a crucial role in water balance computations; the model parameter B (exponent of distribution of soil tension water capacity curve) exhibits sensitivity, suggesting challenges in attaining complete soil saturation across the entire basin. In addition, the insensitivity of the snowmelt module parameters implies that the proportion of snowmelt streamflow is relatively low in the annual streamflow and remains stable. The study results can provide theoretical references for water resource planning and reservoir regulation in the Yellow River Basin.