A method of production of a polyether rubber containing units expressed by the following general formula (1) in 0.1 mol % to less than 30 mol % including reacting a polyether rubber containing epihalohydrin monomer units in 0.1 mol % or more and a nitrogen atom-containing aromatic heterocyclic compound by kneading in the presence of an acid acceptor using an extruder-kneader so as to make at least part of halogen atoms forming the epihalohydrin monomer units be substituted by a group containing a cationic nitrogen-containing aromatic heterocyclic structure is provided. (wherein, in the above general formula (1), A+ is a group containing a cationic nitrogen-containing aromatic heterocyclic structure, where the group containing a cationic nitrogen-containing aromatic heterocyclic structure is bonded with a carbon atom at the “2” position shown in the above general formula (1) through a nitrogen atom forming the cationic nitrogen-containing aromatic heterocyclic structure, and X− is any counter anion.)