Disclosed is a process for producing a diaphragm for a fuel cell comprising a modified anion exchange membrane that substantially maintains durability and hydroxide ion conductivity as an electrolyte membrane and has improved resistance to methanol permeation. The process is characterized by comprising the step of impregnating at least one side of a crosslinked hydrocarbon anion exchange membrane with a polymerizable acidic compound having a weight average molecular weight of not less than 700 and less than 8000, provided that, when the acid site in the compound has been neutralized with a counter cation, the weight of the counter cation is subtracted from the molecular weight, and polymerizing the polymerizable acidic compound.