A method for producing γ-Glu-Val-Gly comprising the step of reacting Val-Gly with a γ-glutamyl group donor in the presence of a γ-glutamyltransferase, a microorganism containing the enzyme, or a processed product thereof to generate γ-Glu-Val-Gly, wherein: the γ-glutamyltransferase consists of a large subunit and a small subunit, and the small subunit has the amino acid sequence of the positions 391 to 580 of SEQ ID NO: 2 or the amino acid sequence having a homology of 90% or more to the foregoing amino acid sequence, and has a mutation corresponding to any one of the following mutations in the amino acid sequence of SEQ ID NO: 2: N411Q, Q430M, Y444D, Y444E, Y444A, G484S, (T413A + Y444E), (T413H + Y444E), (T413N + Y444E), (Q430N + Y444E), (Q430N + Y444D), (Q430N + Y444N), (P441A + Y444E), (V443A + Y444E), (V443E + Y444E), (V443G + Y444E), (V443L + Y444E), (V443N + Y444E), (V443Q + Y444E), (Y444E + L446A), (Y444E + A453S), (Y444E + D472I), (Y444E + G484A), (Y444E + G484S), (Y444E + S498C), (Y444E + Q542H), (Y444E + D561N), (T413N + Y444E + V443A), (T413N + Y444E + A453S), (T413N + Y444E + S498C), (T413N + Y444E + Q542H), (G484S + Y444E + V443A), (G484S + Y444E + Q542H), (Q430N + Y444E + T413N), (T413H + Y444E + G484S), (T413N + Y444E + G484S), (T413N + Y444E + G484S + V443A), (T413N + Y444E + G484S + A453S), (T413N + Y444E + G484S + Q542H), (T413N + Y444E + G484S + S572K) (T413N + Y444E + G484S + Q430N), (T413N + Y444E + G484E + S498C), wherein said processed product contains the mutant enzyme in a state that the mutant enzyme can function, and the processed product is selected from disrupted cells, cell extract, partially purified products thereof, purified enzyme, cell immobilized with acrylamide, carrageenan, and immobilized enzymes comprising the mutant enzyme immobilized on a solid phase. the γ-glutamyltransferase consists of a large subunit and a small subunit, and the small subunit has the amino acid sequence of the positions 391 to 580 of SEQ ID NO: 2 or the amino acid sequence having a homology of 90% or more to the foregoing amino acid sequence, and has a mutation corresponding to any one of the following mutations in the amino acid sequence of SEQ ID NO: 2: N411Q, Q430M, Y444D, Y444E, Y444A, G484S, (T413A + Y444E), (T413H + Y444E), (T413N + Y444E), (Q430N + Y444E), (Q430N + Y444D), (Q430N + Y444N), (P441A + Y444E), (V443A + Y444E), (V443E + Y444E), (V443G + Y444E), (V443L + Y444E), (V443N + Y444E), (V443Q + Y444E), (Y444E + L446A), (Y444E + A453S), (Y444E + D472I), (Y444E + G484A), (Y444E + G484S), (Y444E + S498C), (Y444E + Q542H), (Y444E + D561N), (T413N + Y444E + V443A), (T413N + Y444E + A453S), (T413N + Y444E + S498C), (T413N + Y444E + Q542H), (G484S + Y444E + V443A), (G484S + Y444E + Q542H), (Q430N + Y444E + T413N), (T413H + Y444E + G484S), (T413N + Y444E + G484S), (T413N + Y444E + G484S + V443A), (T413N + Y444E + G484S + A453S), (T413N + Y444E + G484S + Q542H), (T413N + Y444E + G484S + S572K) (T413N + Y444E + G484S + Q430N), (T413N + Y444E + G484E + S498C), wherein said processed product contains the mutant enzyme in a state that the mutant enzyme can function, and the processed product is selected from disrupted cells, cell extract, partially purified products thereof, purified enzyme, cell immobilized with acrylamide, carrageenan, and immobilized enzymes comprising the mutant enzyme immobilized on a solid phase.