Provided is a process for producing a copolymer of diallyldialkylammonium salt and a maleic acid which copolymer is free of residual monomers and polymerization initiator and hence stably exhibits excellent performances in various uses, and the process comprises polymerizing a monomer mixture comprising diallyldialkylammonium salt and maleic acid in the presence of persulfate as a radical polymerization initiator in water or a polar solvent, and completion of the polymerization-reaction, decomposing the radical polymerization initiator to produce a copolymer comprising diallyldialkylammonium salt constituent unit and a maleic acid constituent unit.