Provided is a production method by which an AEI zeolite is obtained without inducing a structural transformation in a crystalline aluminosilicate having a Y-structure and without using fluorine or phosphorus, the method including a crystallization step of crystallizing a composition containing an alumina source, a silica source, a structure directing aunt, a sodium source, and water, a weight proportion of crystalline aluminosilicate relative to a total weight of the alumina source and the silica source being from 0 wt. % to 10 wt. %, and the crystallization step satisfying at least one of the following conditions: a molar ratio of hydroxide ion to silica in the composition is 0.45 or greater, the composition contains a cation represented by (CH3)3RN+ (R represents an alkyl group having from 1 to 4 carbons, and the alkyl group may contain at least one substituent), and the crystallization time is 80 hours or longer.