To obtain a perfluoroalkanesulfonyl fluoride high in electrical efficiency and fluorine utilization efficiency by electrochemically fluorinating an easily obtainable starting material.

This compound, e.g. N,N-bis-methanesulfonimide is obtained by electrochemically fluorinating an alkylmethanesulfonate shown by the formula (RSO2)nX {R is a methyl, ethyl or the like; (n) is 1 to 3; X is -Ri, -ORi or the like; and Ri is R}, e.g. dimethyldisulfonemethylmethanesulfonate in the presence of anhydrous hydrogen fluoride. This reaction prevents the C-S bond cleavage providing a highly toxic SO2F2 from predominating.