Recently, monitoring nuclear materials to avoid nuclear terrorism has become an important area of national security. It can be difficult to detect gamma rays from nuclear material because they are easily shielded by shielding material. Muon tomography using multiple -Coulomb scattering derived from muons can be utilized to detect special nuclear materials (SNMs) such as uranium-235 and plutonium-239. We designed a muon tomography system composed of four detector modules. The incident and scattered muon tracks can be calculated by two top and two bottom detectors, respectively. 3D tomographic images are obtained by extracting the crossing points of muon tracks with a point-of-closest-approach algorithm. The purpose of this study was to optimize the muon tomography system using Monte Carlo simulation code. The effects of the geometric parameters of the muon tomography system on material Z-discrimination capability were simulated and evaluated.