The aim of this work was to predict responses of reference evapotranspiration (ETo) to perturbations of four climatic variables in Shandong province, China. For this purpose, ETo was estimated based on the FAO-56 Penman–Monteith equation, a non-dimensional relative sensitivity coefficient was employed. Climatic variables (i.e., daily air temperature, sunshine duration, wind speed and daily relative humidity) at 12 meteorological stations covering whole area (1960 to 2013) were collected firstly and used for the analysis. Results showed that ETo had positive sensitivities to air temperature, sunshine duration and wind speed, opposite to what were observed to relative humidity. The sensitivity of climatic parameters to ETo showed a decreasing trend: relative humidity> >sunshine duration>wind speed > air temperature. The sensitivity coefficients of different factors varied in time and space. From 1960 to 2013, the sensitivity coefficient of sunshine duration (Sn) showed a downward trend at a rate of (-4.3e-4)/a. The sensitivity coefficient of wind speed (SWS) and relative humidity (SRH) increased at a rate of (3.9e-4)/a and (1.9e-3)/a respectively, while the sensitivity coefficient of air temperature (ST) waved with a tiny decrease trend. The values of ST and Sn in southern were larger than in northern region. The values of SWS in southern and northeast region were smaller than that in the northern area. SRH in the central region was lower than other area, opposite to what were observed in coastal areas.