A method for producing an L-amino acid includes culturing a bacterium which belongs to the family Enterobacteriaceae and has an L-amino acid-producing ability in a medium containing a carbon source selected from a fatty acid and an alcohol, and collecting the L-amino acid from the medium. A bacterium which has been subjected to a modification including at least one of enhancement of oxyS gene expression, enhancement of fixABC gene expression, and combination thereof, is used as the bacterium, or a substance that reduces intracellular hydrogen peroxide concentration of the bacterium is added to the medium.