Hydraulic conductivity (Kψ) is one of the most important soil properties that influences water and chemical movement within the soil and is a vital factor in various management practices, like drainage, irrigation, erosion control, and flood protection. Therefore, it is an essential component in soil monitoring and managerial practices. The importance of Kψ in soil-water relationship, difficulties for its measurement in the field, and its high variability led us to evaluate the potential of stepwise multiple linear regression (SMLR), and multilayer perceptron (MLPNNs) and radial-basis function (RBFNNs) neural networks approaches to predict Kψ at tensions of 15, 10, 5, and 0 cm (K15, K10, K5, and K0, respectively) using easily measurable attributes in calcareous soils. A total of 102 intact (by stainless steel rings) and composite (using spade from 0–20 cm depth) soil samples were collected from different land uses of Fars Province, Iran. The common physico-chemical attributes were determined by the common standard laboratory approaches. Additionally, the mentioned hydraulic attributes were measured using a tension-disc infiltrometer (with a 10 cm radius) in situ. Results revealed that the most of studied soil structure-related parameters (soil organic matter, soluble sodium, sodium adsorption ratio, mean weight diameter of aggregates, pH, and bulk density) are more correlated with K5 and K0 than particle-size distribution-related parameters (sand, silt, and standard deviation and geometric mean diameter of particles size). For K15 and K10, the opposite results were obtained. The applied approaches predicted K15, K10, K5, and K0 with determination coefficient of validation data (R2val) of 0.52 to 0.63 for SMLR; 0.71 to 0.82 for MLPNNs; and 0.58 to 0.78 for RBFNNs. In general, the capability of the applied methods for predicting Kψ at all the applied tensions was ranked as MLPNNs > RBFNNs > SMLR. Although the SMLR method provided easy to use pedotransfer functions for predicting Kψ in calcareous soils, the present study suggests using the MLPNNs approach due to its high capability for generating accurate predictions.