Optical anisotropy (OA) and magneto-optical anisotropy (MOA) in the infrared and visible region for FeCu superlattice were investigated by using first-principles calculations and the electronic origins underlying the optical spectra were elucidated by band-by-band decomposition analysis. We find that the OA spectrum is featured by a prominent peak and dip at around 1.5 and 3.5 eV, and for the MOA spectrum, by three peaks at 0.5, 1.7, and 2.5 eV. For the OA, the strong dd hybridizations between the in-plane Fe-Fe atoms and the weak dd hybridization between Fe and Cu atoms play a role, while for the MOA although the spectrum behaves complicatedly, a change in the orbital m-characters by changing the sample magnetization direction becomes an origin of the MOA.