A bacterium which belongs to the Enterobacteriaceae family and has an ability to produce an L-amino acid such as L-lysine, L-threonine and L-tryptophan and is modified to enhance glutamic acid decarboxylase activity is cultured in a medium to produce and accumulate the L-amino acid in the medium or cells of the bacterium. Then, the L-amino acid is collected from the medium or the cells.