The flowing bottom-hole pressure (FBHP) of an oil well is important information for reservoir engineers and production technologies. It is an essential parameter to enable well production forecasting, production monitoring and well artificial lift system optimization. Therefore, the installation of down-hole gauges in oil wells has become a common practice in the oil petroleum industry; especially in wells lifted with electrical submersible pumps. However, these down-hole gauges require continuous maintenance and calibration. Also, due to the harsh down-hole environment there is a high risk they will fail and will be expensive to repair or replace. In addition, intervening a well from time to time to measure the FBHP is an expensive task and associated with production risk and interruption. For these reasons the motivation of the estimation of the FBHP has come out. Estimating the FBHP of wells with multiphase flow is a challenging and very complex problem. Experience has shown that empirical correlations and mechanistic models failed to provide a satisfactory and reliable tool for estimating pressure drop in multiphase flowing wells. Large errors are usually associated with these models and correlations. The recent development and success of applying artificial neural networks (ANN) to solve various difficult and complex engineering problems has drawn the attention to its potential applications in the petroleum industry. With regard to this field, few researchers applied ANN techniques to resolve some problems associated with multiphase problems including pressure drop estimations. The objective of this study is to develop an ANN model to estimate the FBHP in vertical oil wells by using measured data from oil fields of Oman. This is achieved by designing and developing a multilayer perceptrons feedforward neural network (FFNN) with backpropagation algorithm. The selection of the best number of hidden layers is done through trial and performance assessment. Similarly, the best number of neurons in each hidden layer is selected. Also, a radial basis function neural network model is developed and compared to the single and two hidden layers models performance. The best neural network model performance is also compared against an empirical model developed to calculate the FBHP using available input data. The software package used is the MATLAB Neural Networks Toolbox 2009 edition. Field data is used to train and test the model. Field data has been gathered from pumped oil wells from Oman oil fields. Model inputs data were selected from the list of available surface well measurements. Data is preprocessed prior to training and testing processes. The model performance evaluation conducted by means of testing the model against actual well down-hole measurements data from the same oil fields. These testing data have not been used in the model training. Standard statistical analyses preformed on the results to evaluate the models estimation accuracy such as; root mean square error, standard deviation of error, minimum/maximum/average absolute relative error and correlation coefficient. These statistical analyses have shown that the FFNN has a very strong ability in estimating the FBHP compared to the empirical formula.