Current pedotransfer functions (PTFs) for estimating soil hydraulic curves are mostly developed to predict parameters of the Mualem-van Genuchten hydraulic functions. The Mualem-van Genuchten functions are recognised to be inadequate in representing soil water retention hydraulic conductivity curves at low pressure head ranges. This study presents neuroFX, a suite of PTFs, for estimating soil water retention and unsaturated hydraulic conductivity curves from saturation to complete dryness based on the Fredlund-Xing-Wang (FXW) model. The PTFs were calibrated using the neuro-m neural networks approach with three different sets of inputs: (1) SSCBD uses the sand, silt, and clay fractions, and bulk density; (2) SSC uses the sand, silt and clay fractions, and (3) soil textural class input. NeuroFX PTFs were trained using fitted parameters of the FXW model from selected data in the UNSODA database and validated using 5-fold cross-validation that was repeated 10 times. NeuroFX provides an uncertainty estimate of hydraulic parameters. The prediction quality of neuroFX was compared with two existing PTFs: ROSETTA and Brunswick-Weber (BW) PTFs. Based on multiple criteria, we found that neuroFX performed better than ROSETTA and BW PTFs in the same test sample. NeuroFX PTF with the SSCBD input yielded the best prediction of soil water retention and unsaturated hydraulic conductivity curves with RMSE in water content of 0.052 cm3 cm−3 and RMSE in log10(K) = 0.732 (in the magnitude of cm day−1), indicating the importance of including bulk density in the input of PTFs. NeuroFX was then used to map parameters of the FXW model for the whole of the continental USA over 6 depth intervals. The code of neuroFX in R software is available in Supplementary Material 1.