We investigated the orbital anisotropy of LuFe(2)O(4) using the Fe L(2,3)- and O K-edge x-ray absorption spectroscopy (XAS) and cluster model calculations. X-ray magnetic circular dichroism reveals a surprisingly large orbital magnetic moment (m(o) approximately 0.8 micro(B)/f.u.), which originates the giant magnetic anisotropy. The polarization dependent XAS enables us to identify the orbital states and occupations, different from the band calculation predictions. These findings were examined by using the cluster model analysis, which also explains the orbital magnetic moment as well as the total moment (2.9 micro(B)/f.u.). Taking into account the charge order, we also determined the spin structure.