An Artificial Neural Network (ANN) was designed and tested in the present study to examine the correlation between permeability estimations and porous medium properties, such as porosity, specific surface area, and irreducible water saturation. The network developed in this work is a predictive tool that uses soft computing techniques to estimate absolute permeability of carbonate reservoirs. The Artificial Neural Network toolbox of MATLAB® R2006b and the Feed Forward Error Back Propagation methodology were used in the construction of the network. Carbonate reservoir field data presented in the literature were utilized in the training, testing, and validation of the proposed model. The present study indicates that ANN generated permeability values are consistent with those obtained from core analysis. Results from this study confirm the complex relationship among permeability, porosity, specific surface area and irreducible water saturation of carbonate reservoirs, and suggest that variations in specific surface area affect the magnitude of irreducible water saturations, thus creating an apparent dependence of permeability on irreducible water saturation. Additional observations support a direct relationship between porosity and permeability, and an inverse relationship between specific surface area and permeability.