Muon tomography (MT) based on the measurement of multiple scattering of atmospheric cosmic ray muons traversing shipping containers is a promising candidate for identifying threatening high-Z materials. Since position-sensitive detectors with high spatial resolution should be particularly suited for tracking muons in a MT application, we propose to use compact micro-pattern gas detectors, such as gas electron multipliers (GEMs), for muon tomography. We present a detailed GEANT4 simulation of a GEM-based MT station for various scenarios of threat material detection. Cosmic ray muon tracks crossing the material are reconstructed with a point-of-closest-approach algorithm to form 3-D tomographic images of the target material. We investigate acceptance, Z-discrimination capability, effects of placement of high-Z material and shielding materials inside the cargo, and detector resolution effects for such a MT station.