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Hydrological cycle changes that occur due to a changing environment is a hot topic in the field of hydrological science. It is of great practical significance to study the response mechanism of hydrological process change for future water resources planning and management. In this study, the effects of climate and watershed characteristic change on the streamflow in a typical tributary of the Yellow River (the Fen River watershed) are studied based on the Budyko hypothesis. The results show that: the sensitivity coefficients of streamflow to precipitation, potential evapotranspiration, and the watershed characteristic coefficient were 0.1809, −0.0551, and −27.0882, respectively. This meant that a 1 mm decrease in the precipitation would induce a 0.1809 mm decrease in the streamflow. Additionally, a 1 mm decrease in the potential evapotranspiration would induce a 0.0551 mm increase in the streamflow, and an increase of 1 in the watershed characteristic coefficient would induce a 27.0882 mm decrease in the streamflow. The streamflow of the Fen River watershed showed a significant decreasing trend during the reference period (1951–1977). In addition, the streamflow of the change period (1978–2010) decreased 26.87 mm; and this was primarily caused by watershed characteristic change which accounted for 92.27%, while climate change only accounted for 6.50%.