We present results and methodology for predicting permeability from thin sections. The method consists of two key components--reconstruction of 3D porous media from 2D thin sections, and 3D flow simulation using the Lattice-Boltzmann (LB) technique. We construct 3D porous media using sequential indicator simulation (SIS), a geostatistical method, with conditional data and input statistical parameters from thin sections. Permeability is then estimated through flow simulation on the reconstructed porous media. The LB flow simulation successfully handles very complex reconstructed 3D pore geometries. Computed permeabilities from seven thin section samples show good agreement with laboratory measurements over a wide range of permeability. We compare our method to one that uses only thin sections without 3D reconstruction. The comparison shows that our method gives better prediction of permeability, and is less sensitive to statistical errors from discrepancy between thin sections and core samples.