Representative elementary volume (REV)-scale structure of shale matrix is reconstructed based on elementary building block (EBB) model using a stochastic reconstruction method called Quartet Structure Generation Set. In the EBB model, various constituents with different pore morphologies in shale matrix including organic matter and inorganic minerals are considered as different EBBs, and in each EBB, specific structural parameters and transport properties are locally defined. A generalized lattice Boltzmann model for fluid flow through tight porous media with slippage is employed to simulate fluid flow through the reconstructed REV-scale structures. A four-EBB shale matrix including clay, calcite, pyrite and organic matter is studied and its permeability is predicted. Effects of organic content, grain size, interparticle pores on the permeability of the REV-scale matrix are investigated. It is found that smaller grain size and interparticle pores can increase the permeability. The influences of complex physical processes such as slippage and adsorption on the REV-scale permeability are also explored. Slippage effect increases as the pore size decreases. Adsorption has two opposite effects on the permeability, and which one dominates depend on pressure. The present study can help understand gas transport in shale matrix and improve reservoir scale studies. (C) 2015 Elsevier Ltd. All rights reserved.