Optimal materials to induce bulk photovoltaic effects should lack inversion symmetry and have an optical gap matching the energies of visible radiation. Ferroelectric perovskite oxides such as BaTiO\(_3\) and PbTiO\(_3\) exhibit substantial polarization and stability, but have the disadvantage of excessively large band gaps. We use both density functional theory and dynamical mean field theory calculations to design a new class of Mott multiferroics--double perovskite oxides \(A_2\)VFeO\(_6\) (\(A\)=Ba, Pb, etc). While neither perovskite \(A\)VO\(_3\) nor \(A\)FeO\(_3\) is ferroelectric, in the double perovskite \(A_2\)VFeO\(_6\) a `complete' charge transfer from V to Fe leads to a non-bulk-like charge configuration--an empty V-\(d\) shell and a half-filled Fe-\(d\) shell, giving rise to a polarization comparable to that of ferroelectric \(A\)TiO\(_3\). Different from nonmagnetic \(A\)TiO\(_3\), the new double perovskite oxides have an antiferromagnetic ground state and around room temperatures, are paramagnetic Mott insulators. Most importantly, the V \(d^0\) state significantly reduces the band gap of \(A_2\)VFeO\(_6\), making it smaller than that of \(A\)TiO\(_3\) and BiFeO\(_3\) and rendering the new multiferroics a promising candidate to induce bulk photovoltaic effects.