Evapotranspiration consists of soil evaporation and plant transpiration. It is the main mechanism of the transfer and conversion of energy and moisture occurring in the soil-vegetation-atmosphere system. Potential evapotranspiration (PE) is the theoretical upper limit value of evapotranspiration, reflecting the land surface evapotranspiration capacity under the existing weather conditions. A reasonable estimate of PE is very important for studying climate change, monitoring agricultural drought, improving the utilization rate of agricultural water resources, and for many other purposes. At present, the input parameters of PE calculation models are based mostly on meteorological data. Among the models, the FAO Penman-Monteith (FPM) formula is suitable for both humid and arid/semiarid areas. Thus, FPM is often used as the standard method for calculating PE. This paper is based on daily meteorological data, collected from 28 sites of the study area and the surrounding area in 1975-2012, to estimate potential evapotranspiration by using FPM. The trend-free pre-whitening Mann-Kendall (TFPW-MK) test and sensitivity analysis were used to examine the change law and the factors influencing PE through the years. The spatial distribution characteristics of pixel-based PE and its variation trend were studied using Matlab and ArcGIS. The goal of the study was to provide methods and data support for ecological evaluation, disaster prevention, and agricultural structure adjustment. The conclusions of the study are as follows: 1) The change of average monthly PE from 1975 to 2012 was an inverted U-shaped curve, and the maximum and minimum values appeared in July and January, respectively. The average annual PE of Yanchi and Haiyuan counties showed a slight decreasing trend in 1975-2012, but the average annual PE of Tongxin County grew significantly, with an outstanding PE increase in March, April, and June. 2) In terms of influencing factors, in addition to net radiation, the sensitivity coefficients of various meteorological elements changed little during the study period in Yanchi County. Temperature in Yanchi County increased through the years, but wind speed decreased significantly, which is the main reason for the weak reduction of PE. In Tongxin County, the increase of wind speed, temperature, and its sensitivity coefficient would promote an increase of PE, but the increase of vapor pressure and the decrease of its sensitivity coefficient would help decrease PE. The combined result of both aspects led to significantly increased PE at the interannual scale, which shows that temperature and wind speed play a dominant role for PE in the region. In Haiyuan County, although temperature increased significantly through the years, wind speed decreased significantly, vapor pressure increased, and the temperature sensitivity coefficient decreased, resulting in slightly reduced PE. At the monthly scale, the change of temperature reached its maximum, especially in the growing season of plants (from May to September), and the influence of temperature was significantly higher than those of other factors. 3) PE in the study area had an obvious spatial variation law. PE in Yanchi County showed a decreasing trend with increasing longitude, and PE in Tongxin and Haiyuan counties showed an increasing trend with increasing latitude. For the spatial characteristics of the PE variation trend, the range of Z value calculated by the Mann-Kendall test for each pixel was -1.65-2.47 in Yanchi County, but the change of PE in most of the region was not obvious. Regions with significantly increased PE accounted for only 2.52% of the total area of the county. In Tongxin County, the range of Z value was 0.50-3.70, and significantly and extremely significantly increased areas accounted for 61.98% of the county. The range of Z value in Haiyuan County was from -0.70 to 3.73, and the PE variation trend of the county was a slight decrease or weak increase. The ratio of significantly increased areas was less than 30.00%.