In this work, a novel approach based on an artificial neural network (ANN) was used to develop a model for analyzing, correlating, and producing relationships between the oil recovery efficiency and the limestone porosimetry data collected from drilling cores. The focus in this research work is to build a general model to predict limestone core recovery efficiency based on basic laboratory measurements such as pores surface area, mean pore-entry diameter, pore-size distribution characterized by pore population modes, and porosity values. The model was trained using a large number of core sample data (497 cases) for the above listed variables, and their corresponding recovery efficiency resulting from core sample experiments. Model validation and testing results showed that the model predicted the recovery efficiency with a high degree of accuracy of 93.53% and a mean absolute percentage error of 6.47 when compared to actual results. These results were based on testing 82 randomly selected cases from the limestone porosimetry data collected from the drilled cores. These data were not used in the model’s training. The results, hence, demonstrate the generalization capability of this novel approach over unseen data and its ability to produce accurate predictions.