To provide an anion exchanger having sufficient ion exchange quantity and a high adsorption rate.

This method for producing the anion exchanger includes a process for irradiating a polymer base material, which comprises a repeating structure unit having at least one hydroxy group, with ionizing radiation, and a process for introducing a graft chain having a quaternary ammonium group into the polymer base material by bringing the polymer base material irradiated with ionizing radiation into contact with a monomer having the structure represented by general formula (I) or a general formula (A). In the formula, R3 is a 1-8C alkylene group, and X is a halogen atom.