the present invention provides a method for producing a fluorine - containing alkane , which comprises reacting at least one fluorine - containing compound selected from the group consisting of chlorine - containing fluoroalkanes and fluorine - containing alkenes with hydrogen gas in the presence of catalysts , wherein two or more catalysts having different catalytic activities are used , and the fluorine - containing compound and hydrogen gas , which are starting materials , are sequentially brought into contact with the catalysts in the order of the catalyst having a lower catalytic activity followed by the catalyst having a higher catalytic activity . according to the present invention , in the method for producing a fluorine - containing alkane by using chlorine - containing fluoroalkane or fluorine - containing alkene as a starting material , and subjection it to a reduction reaction or a hydrogen addition reaction , the objective fluorine - containing alkane can be produced with high productivity .