There is provided an anion exchange membrane comprising, as a main element, a block copolymer having a vinyl alcohol polymer block and a cationic-group containing polymer block as components and which is subjected to a crosslinking treatment. An anion exchange membrane is produced by heating a film obtained from a solution of the block copolymer at a temperature of 100° C. or more, crosslinking the film with a dialdehyde compound in water, an alcohol or a mixture of these under an acidic condition and then washing the film with water. Thus, there can be provided an anion exchange membrane in which organic fouling can be prevented and which exhibiting excellent basic properties such as a membrane resistance and an ionic transport number and excellent membrane strength.