A new predictive approach based on artificial neural networks (ANN) and wellbore numerical simulation for the determination of pressure drops in flowing geothermal wells was successfully carried out. Several ANN computational models based on the Levenberg-Marquardt optimization algorithm, and the hyperbolic tangent sigmoid and linear transfer functions were evaluated. Two ANN models (ANN(1) and ANN(2), characterized by using five and six input variables, respectively; and a common structure of 9 neurons in the hidden layer) were found to be the most suitable architectures for a reliable determination of geothermal pressure gradients. These ANN models used a limited number of input variables which are commonly available in field measurements (e.g., wellbore production data: pressure, temperature and mass flow rate; and wellbore geometry data). Such ANN models were effectively trained by using a wellbore production database which was compiled from several world geothermal fields. Additional wellbore simulation works were also carried out by using the same production data and a numerical simulator (GEOWELLLS). The pressure gradients predicted by using all these computing tools (ANNs and GEOWELLS) were statistically compared with measured field data. From this matching analysis, it was demonstrated that the ANN2 model provided the most acceptable results (with average prediction errors less than 2.3%) in comparison with those results inferred from ANN(1) and GEOWELL tools. Details of the computational methodology developed in this study, as well as the numerical validation, and the comparative statistical analysis are comprehensively described.