Pore pressure is a fundamental parameter in petroleum engineering. Failure to determine this parameter correctly and accurately can lead to serious problems, such as well blowouts during drilling or incorrect reservoir modeling. On the other hand, empirical methods of calculating pore pressure are generally based on compressional slowness data obtained from conventional sonic logs, which have a limited vertical resolution of about 0.1 m. Consequently, thin features with significant pore pressure variations may not be identified. To address this problem, the present study first estimated compressional slowness with a vertical resolution of 0.005 m using diverse Nuclear Magnetic Resonance (NMR) log data in Well No. 6 of the Binaloud oil field, and then calculated pore pressure using this slowness. For this purpose, NMR log data and compressional slowness from the conventional sonic log were employed to design a multilayer perceptron neural network that predicts compressional slowness from NMR parameters. In the validation stage, the network was able to estimate compressional slowness with a correlation coefficient of 0.94 and a relative error of 0.03. By generalizing the neural network to all depths containing NMR data, high-resolution compressional slowness was calculated in the depth interval of 2179 to 2275 m within the Burgan Formation. Subsequently, pore pressure was estimated using Eaton’s equation, which employed both sonic log data and compressional slowness. According to the resulting pore pressure profile, normal pressure conditions are maintained down to approximately 1700 m, whereas at greater depths, overpressure occurs heterogeneously down to the bottom of the well. This study also demonstrated that using high-resolution estimated slowness enabled the identification of variations up to 50 psi in the well, which could not have been detected without these data.