Abstract: Using the daily data during 1951-2014 from 17 meteorological stations in Heihe River watershed and the surrounding areas, uncertainty analysis of potential evapotranspiration (ET₀) and its influencing factors were studied based on cloud model, which is a mathematical representation of a qualitative concept and integrates the fuzziness and randomness of a qualitative concept in a unified way. Meanwhile, the causes of ET₀ change were manifested by path analysis. The results showed that annual variation in ET₀ had a fluctuating increase tendency. The homogeneity and stability of ET₀ were worse in space than in time, indicating that the temporal distribution of ET₀ was more uniform and stable. Further analysis found that entropy (E_n) and hyper entropy (H_e) of meteorological elements had smaller extents of variation, indicating that the spatial distributions of meteorological elements were uniform and stable. However, the spatial distribution of E_n and H_e differed greatly with the spatial distribution of expected value (E_x). Spatially, the ET₀ increased from the south of Heihe River to the north; this pattern was similar to mean temperature, sunshine hours and wind speed, and was opposite to relative humidity. Relative humidity was the main influencing factor of ET₀, followed by wind speed and temperature. The wind speed and relative humidity had the largest direct effect on the ET₀, while the relative humidity and mean temperature had the largest indirect effect on the ET₀. The negative effect of air temperature and relative humidity on ET₀ by wind speed was obvious.