Oil or fat compositions contain the following ingredients: (A) an oil or fat containing from 60 to 100% by weight of diglyceride, by 100 parts by weight of the oil or fat composition, the diglyceride further comprising fatty acids, wherein the amount of fatty acids that are unsaturated is from 80 to 100 wt. %, by 100 parts by weight of the diglyceride; (B) from 0.001 to 1% by weight of ingredient (A) of a carboxylic acid selected from C.sub.2-8 hydroxycarboxylic acids, dicarboxylic acids and tricarboxylic acids, and salts derivatives thereof, and mixtures thereof; (C) from 0.001 to 5% by weight of ingredient (A) of an antioxidant; and (D) from 0.05 to 4.7% by weight of ingredient (A) of a plant sterol. Each of these preferred oil or fat compositions has a high diglyceride content having excellent health-promoting functions, and even in cold temperature areas or high-humidity areas, has improved external appearance, is good in work efficiency during cooking and also in the flavor and texture of cooked foods. Packaged edible oils or fats are also disclosed.