An accurate prediction of well flowing bottom-hole pressure (FBHP) is highly needed in petroleum engineering applications such as for the field production optimization, cost per barrel of oil reduction, and quantification of workover remedial operations. A good number of empirical correlations and mechanistic models exist in the literature and are frequently used in oil industry to estimate FBHP. But majority of the empirical models were developed under a laboratory scale and are therefore inaccurate when scaled up for the field applications. The objective of this study is to present a new computational intelligence-based model to predict FBHP for a naturally flowing vertical well with multiphase flow. The present study shows that the accuracy of FBHP estimation using PSO-ANN is better than the conventional ANN model. A small average absolute percentage error of less than 2.1% is observed with the proposed model, while comparing the previous empirical correlations and mechanistic models on the same data gives more than 15% error. The new model is trained on a surface production data, which makes the prediction of FBHP in a real time. A group trend analysis tests were also carried out to assure that the proposed model is accurately capturing the underline physics behind the problem.