The invention relates to the use of a-linolenic acid, a-linolenic acid-containing vegetable oils, and combinations thereof, optionally in combination with cinnamon or a cinnamon bark extract, for preventing, treating, or supporting the treatment of diseases associated with an increased glucose and/or HbA1c concentration in the blood, particularly type 2 diabetes mellitus, diabetic retinopathy, maculopathy and neuropathy, and metabolic syndrome.