In order to construct a unified permeability prediction model for multi-stage tight gas sandstones with permeability across 6 orders of magnitude and changeable porosity-permeability relationship, Bayesian regularization neural network is properly configured with core porosity, conventional logs and a few derivates of them as input items. With high accuracy and excellent generalization, it is promising to be stably and reliably popularized in the study area. The way of model construction, optimization and evaluation may provide underlying insights needed for permeability prediction of similar reservoirs and application of machine learning in reservoir evaluation. •No consistent porosity-permeability relation exists in channel sandstones.•Universal permeability model is built with Bayesian regularization neural network.•Sufficient petrophysical-geological information is contained in logs.•Prior knowledges enhance interpretability, controllability and applicability.