Characterizing the lunar radiation environment is essential for preparing future robotic and human explorations on lunar bases. Galactic cosmic rays (GCR) represent one source of ionizing radiation at the Moon that poses a biological risk. Because GCR are charged particles, their paths are affected by the magnetic fields along their trajectories. Unlike the Earth, the Moon has no strong, shielding magnetic field of its own. However, as it orbits Earth, the Moon traverses not only the weak interplanetary magnetic field but also the distant magnetic tail of Earth’s magnetosphere. We combine an empirical magnetic field model of Earth’s magnetosphere with a fully-relativistic charged particle trajectory code to model and assess the access of GCR at the Moon’s orbit. We follow protons with energies of 1, 10 and 100 MeV starting from an isotropic distribution at large distances outside a volume of space including Earth’s magnetosphere and the lunar orbit. The simulation result shows that Earth’s magnetosphere does not measurably modify protons of energy greater than 1 MeV at distances outside the geomagnetic cutoff imposed by Earth’s strong dipole field very near to the planet. Therefore, in contrast to Winglee and Harnett (2007), we conclude that Earth’s magnetosphere does not provide any substantial magnetic shielding at the Moon’s orbit. These simulation results will be compared to LRO/CRaTER data after its planned launch in June 2009.