Abstract The use of technology and planning in agricultural production is essential in Northeastern Brazil, which is the region of the country that most suffers from water shortage. For the best irrigation management, it is necessary to know the potential evapotranspiration rate for water control in order to increase productivity. There are several direct and indirect methods for estimating evapotranspiration, but the standard method recommended by the United Nations Agriculture Organization (FAO) is the Penman-Monteith (PETpm) method because it has higher accuracy than other methods. However, it is a difficult method to be used due to the need for a large number of meteorological elements. In this context, the objective of this study was to estimate potential evapotranspiration by the Penman-Monteith method in the micro-region of Baixo Parnaíba in Maranhão state using artificial neural networks. Agro-meteorological data were collected daily over 34 years, from 1984 to 2017, and these data were obtained from the NASA/POWER website. Subsequently, liquid radiation and potential evapotranspiration were calculated by the Penman-Monteith standard method (1998). To predict potential daily evapotranspiration, the Multi-Layer Perceptron (MLP) was chosen, which is a traditional Artificial Neural Network. The period that presented a higher evapotranspiration index was the same one that showed precipitation with a lower volume and higher temperatures. The artificial neural network model that best adapted to estimate PETpm was MLP 2-5-1. It is concluded that artificial neural networks estimate with accuracy and precision the Penman-Monteith daily potential evapotranspiration of the Lower Parnaiba in Maranhão, and potential evapotranspiration can be estimated by the Penman-Monteith method using neural networks with inputs of air temperatures.