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Mountainous regions are important sources of freshwater. Measurement of actual evapotranspiration (ET) is difficult to obtain in high mountain regions because of the harsh natural environment, and potential ET (PET) is therefore a suitable term to describe the atmospheric water demand of land surfaces under given meteorological conditions in those high elevation areas. In situ measured meteorological data were collected in 2015 and 2016 from five meteorological stations at various elevations from 2980 m to 4484 m in the Qilian Mountains, northwestern China, and the meteorological factors changed markedly with elevation. PET calculated with the Penman method showed a significant elevational gradient, and decreased as the elevation increased. The sensitivity analysis indicated that over the whole period, PET in the research region was most sensitive to net radiation (RN), followed by relative humidity (RH), air temperature (T), wind speed (WS) and soil heat flux (G). When RN was positive, the sensitivity of PET to RN decreased as the elevation increased, and when RN was negative, the sensitivity increased as the elevation increased. When T was above 0 degrees C, the sensitivity of PET to T decreased as the elevation increased, and when T was below 0 degrees C, the sensitivity increased as the elevation increased. The higher the elevation, the greater the sensitivity of PET to both RH and WS. The topographic shading in mountainous regions affected meteorological factors, PET and its sensitivity to meteorological factors in those high elevation areas. The RN was relatively small at the sites with topographic shading because of the reduction in solar radiation, and resulted in less sensitivity of PET to RN and greater sensitivity of PET to other meteorological factors. This study can help us to understand PET in the Qilian mountains and in other mountain regions from which meteorological data are difficult to obtain and very sensitive to climate change.