The production process of the present invention for a chlorine-containing fluorine-containing compound is characterized in that a reaction of adding chlorine atoms to a carbon-carbon unsaturated bond of a hydrogen-containing compound having a carbon-carbon unsaturated bond is carried out under the presence of a fluorine gas. The hydrogen-containing compound having a carbon-carbon unsaturated bond may be 3,4-dichlorobutene-1. Further, the present invention provides a process for producing efficiently and economically 1,2,3,4 -tetrachlorohexafluorobutane from 3,4-dichlorobutene-1 described above. According to the present invention, chlorination and fluorination of the hydrogen-containing compound having a carbon-carbon unsaturated bond are carried out in a single step, and therefore a chlorine-containing fluorine-containing compound can be more economically produced at a higher yield than in a conventional process in which two reactions are individually carried out.