Evapotranspiration is an important component of the terrestrial water cycle, and is complex in cold and arid environments. The northern slope of the Kunlun Mountains in Xinjiang of China, situated on the northern edge of the Qinghai-Xizang Plateau, lacks a comprehensive understanding of potential evapotranspiration due to the absence of long-term meteorological observations. This study examined the spatiotemporal variations of potential evapotranspiration from 1979 to 2021, especially from a sub-basin perspective, and analyzed the relationship between potential evapotranspiration and other meteorological parameters using the Mann-Kendall test and empirical orthogonal function. The results indicate that: (1) The long-term mean of potential evapotranspiration is 733.5 mm per year, exhibiting a spatial variation trend that decreases gradually from the southern edge of the Tarim Basin towards the south. (2) From 1979 to 2021, the mean potential evapotranspiration has increased by 8.7 mm·(10a)^-1. Before 2007, there was an increasing trend, although a decreasing trend can be seen after 2007. (3) Among the six sub-basins, i.e., the Kaxgar River Basin, the Yarkant River Basin, the Hotan River Basin, the Keriya River Basin, the Qarqan River Basin and the Kumkol Basin, the Qarqan River Basin has the highest annual mean potential evapotranspiration of 810.8 mm and the highest linear trend of 11.4 mm·(10a)^-1. In contrast, the linear trends in the Hotan River Basin (4.9 mm·(10a)^-1) and the Keriya River Basin (5.0 mm·(10a)^-1) are lower. In the future, efforts should be made to enhance hydro-meteorological observations in high-altitude regions of the northern slope of the Kunlun Mountains in Xinjiang to understand hydrological uncertainties under the background of global change.