An industrially advantageous process for the production of (3R,4S)-3-cyclopropylaminomethyl-4-fluoropyrrolidine or an enantiomer thereof that is useful as an intermediate for the production of novel antimicrobial agents 10-(3-cyclopropylaminomethyl-4-fluoropyrrolidinyl)pyridobenzoxazine carboxylic acid derivatives.Highly stereoselective asymmetric hydrogenation of 1-protected-4-alkoxycarbonyl-3-oxopyrrolidine, followed by ester hydrolysis, followed by amidation with cyclopropylamine gives crude crystals. The crude crystals are purified by recrystallization to give a novel compound (3R,4S)-1-protected-3-cyclopropylcarbamoyl-4-hydroxypyrrolidine or an enantiomer thereof at high optical purity. The use of these intermediates enables industrial production of high-quality products of (3R,4S)-3-cyclopropylaminomethyl-4-fluoropyrrolidine or an enantiomer thereof. The process is highly simple and can produce the desired products at high purity and stable yields.