FAO56-PM is the standard method for estimating potential evapotranspiration. However, the meteorological data required by the FAO56-PM method are not always available at a given station. This paper evaluated four existing methods and developed a temperature and radiation data-based RBF neural network model. We compared the performance of two temperature-based methods (Hargreaves method and Mc Cloud method) and two radiation-based methods (Priestley-Taylor method and Makkink method) with the FAO56-PM in five typical areas (Anyang, Xinxiang, Zhengzhou, Zhumadian, Xinyang) in Henan Province, China. The results of uncalibrated methods show that the Makkink method performs well while larger biases occur for the other methods. Calibration methods were performed for the Xinxiang data, the results show that lower error of all the methods compared to the uncalibrated methods. Besides, the temperature and radiation data-based RBF neural network model in Xinxiang is of high precision of prediction, and it can be used for the prediction of evapotranspiration.