This paper presents a new approach to simplify the design of class-E power amplifier (PA) using hybrid artificial neural-optimization network modeling. The class-E PA is designed for wireless power transfer (WPT) applications to be used in biomedical or internet of things (IoT) devices. Artificial neural network (ANN) models are combined with optimization algorithms to support the design of the class-E PA. In several amplifier circuits, the closed form equations cannot be extracted. Hence, the complicated numerical calculations are needed to find the circuit elements values and then to design the amplifier. Therefore, for the first time, ANN modeling is proposed in this paper to predict the values of the circuit elements without using the complex equations. In comparison with the other similar models, high accuracy has been obtained for the proposed model with mean absolute errors (MAEs) of 0.0110 and 0.0099, for train and test results. Moreover, root mean square errors (RMSEs) of 0.0163 and 0.0124 have been achieved for train and test results for the proposed model. Moreover, the best and the worst-case related errors of 0.001 and 0.168 have been obtained, respectively, for the both design examples at different frequencies, which shows high accuracy of the proposed ANN design method. Finally, a design of class-E PA is presented using the circuit elements values that, first, extracted by the analyses, and second, predicted by ANN. The calculated drain efficiencies for the designed class-E amplifiers have been obtained equal to 95.5% and 91.2% by using analyses data and predicted data by proposed ANN, respectively. The comparison between the real and predicted values shows a good agreement.