Muon tomography (MT) based on the masurement of multiple scattering of atmospheric cosmic ray muons traversing containers is a promising candidate for identifying threatening made of high-Z material such as uranium and certain special nuclear material might be successfully smuggled across international borders by shielding the emanating radiation to evade detection by the standard radiation portal monitors currently operating at borders and ports. 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.