A yeast which harbors a mutant glutathione synthetase having one or both of mutations selected from the group consisting of a mutation to replace a threonine residue at the position 47 with an isoleucine residue and a mutation to replace a glycine residue at the 387-position with an aspartic acid residue and produces γ-glutamylcysteine. The yeast is cultured under suitable conditions, the resultant culture or fractionation product thereof or the resultant culture or fractionation product thereof that had been heat-treated is mixed with food or beverage materials and processed into foods or beverage to produce γ-glutamylcysteine- or cysteine-containing foods or beverage.