Process for extracting unwanted acidic compounds from a drinkable liquid, and in particular from a wine, which comprises the following operative steps: - arranging, in a first tank (2), a drinkable liquid to be treated (L) comprising at least one unwanted acidic compound; - conveying the drinkable liquid to be treated (L) to a membrane separation unit (3); - separating, in the membrane separation unit (3), the drinkable liquid to be treated (L) into a retentate (R) and a permeate (P), with the unwanted acidic compound mainly contained in the permeate (P); - adjusting the conductivity of the permeate (P) at a minimum threshold value greater than 200 µS susceptible to dissociate at least a fraction of the unwanted acidic compound into corresponding ions; - subsequently flowing the permeate (P) through an electrodialysis unit (6), with extraction of at least one part of said ions, to obtain at least one concentrate (C), containing the aforesaid ions, and at least one deacidified permeate (Pd) substantially without such ions; - mixing the deacidified permeate (Pd) with the retentate (R) to obtain the deacidified final drinkable liquid. Also forming the object of the invention is a plant for executing the above-described process for extracting unwanted acidic compounds from a drinkable liquid.