On the basis of first-principles calculations, we design a novel Cr-based metal-organic framework to be both multiferroic and magnetoelectric. The compound shows a "double-hybrid" nature: it is a hybrid organic-inorganic compound and it shows hybrid improper ferroelectricity. Here, the coupling of non-polar distortions, such as Jahn-Teller pseudo-rotations and tilting, pave the way to a polar behavior, with the coupling being realized through hydrogen bonds.