The phenomenon of evapotranspiration (ET) is closely linked to the issue of water scarcity, as it involves water loss through both evaporation and plant transpiration. Accurate prediction of evapotranspiration is of utmost importance in the strategic planning of agricultural irrigation, effective management of water resources, and precise hydrological modeling. The current investigation aims to predict the monthly ET values in the Elazig province by developing an artificial neural network (ANN) model utilizing the Levenberg–Marquardt method. Consequently, the values of temperature, precipitation, relative humidity, solar hour, and mean wind speed were utilized in forecasting evapotranspiration values by implementing ANN algorithms. This research makes a valuable contribution to the existing body of literature by utilizing an ANN model developed with the Levenberg–Marquardt method to estimate evapotranspiration. It has been discovered that evapotranspiration values are impacted by various factors such as temperature (minimum, average, maximum), relative humidity (minimum, average, maximum), wind speed, solar hour, and precipitation values, which are taken into consideration for prediction. The findings indicated that Elazig, Keban, Baskil, and Agin sites had R values of 0.9995, 0.9948, 0.9898, and 0.9994 in the proposed model. It was found that Elazig’s MAPE ranged from 0 to 0.2288, Keban’s was 0.0001 to 0.3703, Baskil’s was between 0 and 0.4453, and Agin’s was both 0 and 0.2784. The findings obtained from the proposed model are compatible with evapotranspiration values computed from the Hargreaves method (R2 = 0.996). The study’s findings provide significant insights for planners and decision-makers involved in the planning and managing water resources and agricultural irrigation.