Process for the elimination of mercury contained in a heavy hydrocarbon-containing feedstock upstream of a main fractionation unit, a process in which: a) the non-elemental mercury contained in the compounds of said feedstock is transformed to elemental mercury, b) a separation of the feedstock obtained in stage a) is carried out in a separation unit, that consists of producing a liquid effluent and a gaseous effluent comprising elemental mercury; c) the gaseous effluent originating from stage b) comprising the elemental mercury is brought into contact with a mercury capture material contained in a unit for the capture of mercury, in order to produce an effluent that is at least partially de-mercurized.