The headwater region of the Yellow River (HRYR) is one of the most important water supply areas of the whole river basin, which has suffered a serious water shortage problem for recent years. A better understanding of impacts of climate and catchment changes on runoff variation will help to determine efficient measures to deal with the runoff reduction in the Yellow River. The Budyko complementary relationship between the partial elasticity of runoff (R) with respect to precipitation (P) and that with potential evapotranspiration (E0) was used in this study to partition the effects of climate and catchment changes on runoff variation at the HRYR. The upper and lower bounds of the contributions of climate and catchment changes to runoff variation were determined for every five years during 1961–2010. Results show that the complementary relation method based on the Budyko hypothesis can partition the contributions of climate and catchment changes to runoff variation effectively. And the climate changes are the main reasons (account for 60%–70% of the runoff variation) for runoff reduction at the HRYR. The sensitivity coefficient of R with respect to P has a significant decreasing trend at the 0.05 level with arid ratio (E0/P) and that with respect to E0 has a significant increasing trend at the 0.05 level with E0/P, indicating that with drying climate, R becomes more insensitive to climate changes. More precipitation is consumed by evapotranspiration returning to the atmosphere, leading to the runoff reduction at the HRYR.