Double perovskite oxides Sr2MoBO6 (B=Os,Re,W) have been predicted to be half metals with high magnetic ordering temperature. In this work, the electronic structure and optical properties of Sr2MoBO6 were calculated by first-principles method, and the intrinsic relationships between them were also discussed. From the energy band structure, Sr2MoOsO6 and Sr2MoWO6 are half metals, and Sr2MoReO6 is a normal metal. The imaginary part ε2(ω) of the complex dielectric function of Sr2MoBO6 all have obvious dielectric peaks in the visible region due to the transition process between B 5d and Mo 4d. Further, the three compounds all have a wide absorption spectrum and a high absorption coefficient. Among them, the absorption spectra of Sr2MoReO6 and Sr2MoWO6 stretch across the whole visible region and even extend to the infrared band. The highest absorption coefficient of Sr2MoReO6 in the visible region is 41.86×104 cm-1, and one of the absorption peaks is located at 886 nm. The absorption peak of Sr2MoWO6 is at 780 nm and the peak absorption coefficient is 41.62×104 cm-1. In addition, Sr2MoBO6 have high reflectivity in the whole range of visible region. The peak reflectivity of Sr2MoWO6 can reach up to 0.55. The response of Sr2MoBO6 to visible light indicates that they have a wide application prospect in the field of optoelectronic devices.