Potential evapotranspiration (ET_0) is generally accepted to be an important element of the hydrological cycle, and changes in sensitivity coefficients of ET_0 to climate variables are of great significance for agricultural water use planning, irrigation system design and management, especially under the condition when climate change may have important influence on water-shortage regions, such as Yellow River basin (YRB), where warmer and drier conditions might augment water demand by crop. However, little reports have focused on the related issues in the upper, middle, and lower regions of YRB. Therefore, this study aimed to investigate the variation of ET_0 and its response to climate variables in the upper, middle, and lower regions of YRB. Based on data for 109 meteorological stations in and around YRB from the Chinese Meteorological Administration (CMA) in years of 1961-2012, ET_0 was estimated using the Penman-Monteith equation recommended by Food and Agricultural Organization (FAO-56) and its sensitivity coefficient to climate variables (solar radiation, relative humidity, daily air temperature, and wind speed) was calculated. The results showed that the average daily ET_0 value in upper region was higher than in the middle and lower region of YRB and a significantly decreasing trend of ET_0 was detected with the magnitude of 0.043 mm per decade in lower region. The diurnal variation curve of solar radiation, air temperature and their sensitivity coefficients was in a single apex type in the upper, middle and lower regions of YRB, and that the sensitivity coefficients of wind speed changed following a single trough type curve. However, the curves fluctuated largely for relative humidity, wind speed along with sensitivity coefficient for relative humidity and air temperature. Furthermore, the maximum value of sensitivity coefficient for relative humidity was found in December, similarly for air temperature and solar radiation in July and August, respectively. A decreasing trend was observed for solar radiation, relative humidity, wind speed and sensitivity coefficient of solar radiation and air temperature. But, an increasing trend was detected for air temperature, sensitivity coefficient of relative humidity and wind speed in recent 52 years. Relative humidity is considered to be the most sensitive variable, while solar radiation is recognized as primarily controlling variable for ET_0 in the whole year and recent 52 years. Moreover, the high value of sensitivity coefficients to solar radiation, relative humidity and air temperature was found in the southwest study area, while the high value of sensitivity coefficients to wind speed was in the north region. Therefore, the southwest region was recognized as the most sensitive region for response of ET_0 to climate change. The findings from this research provide important information for crop planting adjustment, ecological engineering planning and water-soil resource management in YRB in an attempt to improving the healthy development of agriculture and ecological environment.