Muon tomography is a useful method for monitoring special nuclear materials (SNMs) such as spent nuclear fuel inside dry cask storage. Multiple Coulomb scattering of muons can be used to provide information about the 3-dimensional structure and atomic number(Z) of the inner materials. Tomography using muons is less affected by the shielding material and less harmful to health than other measurement methods.We developed a muon detector for muon tomography, which consists of a plastic scintillator, 64 long wavelength-shifting (WLS) fibers attached to the top of the plastic scintillator, and silicon photomultipliers (SiPMs) connected to both ends of each WLS fiber. The muon detector can acquire X and Y positions simultaneously using a position determination algorithm.The design parameters of the muon detector were optimized using DETECT2000 and Geant4 simulations, and a muon detector prototype was built based on the results. Spatial resolution measurement was performed using simulations and experiments to evaluate the feasibility of the muon detector. The experimental results were in good agreement with the simulation results. The muon detector has been confirmed for use in a muon tomography system.