Naturally fractured reservoirs have been studied extensively in the past decades. These reservoirs consist of two distinct porous media: the macropores and the micropores. Several analytical models have been suggested to characterize such reservoirs. In this work, one of the proposed double-porosity pressure transient models is adopted in the description of the naturally fractured reservoirs. The forward solution component of the analytical model is used to generate the pressure transient data, given the characteristic parameters of the double-porosity reservoirs. The double-porosity systems are characterized by a pressure transient signature which is composed of two semi-log straight lines connected by a transitional curve. The pressure transient responses obtained by the analytical forward solution are subjected to a polynomial fit algorithm so that the aforementioned double-porosity signature can be represented by five polynomial coefficients. These coefficients, the known properties of the double-porosity reservoir, and the reservoir fluid and well parameters constitute the principal input given to the artificial neural network (ANN) during the training phase. The ANN, then, inversely predicts the desired unknown properties of the double-porosity system, namely the permeability of the fracture, the porosity of the matrix, the porosity of the fracture, and the permeability of the matrix. This final development of the ANN is achieved by utilizing this inverse protocol in gradually increasing levels of complexity. The complexity of the problem is elevated by increasing the number of unknown characteristics of the double-porosity system. This research demonstrates the efficiency of the ANN utilization in obtaining the desired properties of the double-porosity reservoirs.