The evaluation of pressure drops across the length of production wells is a crucial task, as it influences both the cost-effective selection of tubing and the development of an efficient production strategy, both of which are vital for maximizing oil recovery while minimizing operational expenses. To address this, our study proposes an innovative hybrid intelligent system designed to predict bottom-hole flowing pressure in vertical multiphase conditions with superior accuracy compared to existing methods using a data set of 150 field measurements amassed from Algerian fields. In this work, the applied hybrid framework is the Adaptive Neuro-Fuzzy Inference System (ANFIS), which integrates artificial neural networks (ANN) with fuzzy logic (FL). The ANFIS model was constructed using a subtractive clustering technique after data filtering, and then its outcomes were evaluated against the most widely utilized correlations and mechanistic models. Graphical inspection and error statistics confirmed that ANFIS consistently outperformed all other approaches in terms of precision, reliability, and effectiveness. For further improvement of the ANFIS performance, a particle swarm optimization (PSO) algorithm is employed to refine the model and optimize the design of the antecedent Gaussian memberships along with the consequent linear coefficient vector. The results achieved by the hybrid ANFIS-PSO model demonstrated greater accuracy in bottom-hole pressure estimation than the conventional hybrid approach.