Sr2CrOsO6 has the highest magnetic transition temperature (725 K) among the double perovskite oxides. Ca2CrOsO6 was obtained by replacing Sr ions with smaller volume Ca ions, and the magnetic transition temperature was higher than room temperature. Further substitution of Cr ions by Mo ions with more delocalized d orbitals yielded Ca2MoOsO6. The electronic structures and magneto-optical Kerr effects of the double perovskite oxides Sr2CrOsO6, Ca2CrOsO6 and Ca2MoOsO6 have been systematically calculated by density functional theory. The electronic structures indicate that all three materials are semiconductors. The electronic structures of Sr2CrOsO6 and Ca2CrOsO6 are very similar, and the band gap of Ca2MoOsO6 is extremely small, only 0.10 eV. Observing the magneto-optical Kerr effect line, all three materials show significant magneto-optical Kerr effects in the range of infrared to visible spectrum. The maximum Kerr rotation angles of Sr2CrOsO6, Ca2CrOsO6 and Ca2MoOsO6 are 1.18°, 0.98° and 0.65°. The maximum Kerr rotation angle of the three materials is greater than 0.2°, which makes them to be ideal magneto-optical materials. The calculated results show that the inclusion of both 3d(4d) and 5d transition metal ions in the compound contributes to the significant magneto-optical Kerr effect. Analysis of the optical conductivity tensor shows that the peak of the magneto-optical Kerr line of three materials originates from the interband transition and is dominated by the imaginary part of the off-diagonal element of optical conductivity tensor.