The magneto-optical polar Kerr effect of L10-type ordered alloys TM-X (TM = Mn, Fe, Co, X = Pt, Au) was calculated from the electronic structures given by the first-principles LMTO-ASA method. The calculated results agreed reasonably well with the experimental results. The important optical transitions were clarified by detailed analysis of the electronic structures. For example, it was found that the peak structure at about 4 eV in the Kerr spectra of L10-FeAu mainly originated from the d↓→f↓ transition on Au. In this transition, the final state Au (f↓) is a small tail state hybridized with the unoccupied Fe (3d↓) state. Thus, the transition can simply be expressed as the Au (5d↓)→Fe (3d↓) transition.