The present invention relates to a production method of an oil containing triglyceride in which medium chain fatty acids are bound to the 1- and 3-positions of the triglyceride and polyunsaturated fatty acid is bound to the 2 position by allowing lipase, which specifically acts on ester bonds at the 1- and 3-positions that has been immobilized on a porous ion exchange resin support having a pore size of about 100 Angstroms or more, to act on a mixture of medium-chain fatty acids and raw material oil containing at least one polyunsaturated fatty acid selected from the group consisting of .omega.6 series polyunsaturated fatty acid having 18 or more carbon atoms and 3 or more double bonds and .omega.9 series polyunsaturated fatty acid having 18 or more carbon atoms and 2 or more double bonds, but not containing .omega.3 series polyunsaturated fatty acid, oils and fats or triglycerides obtained by that method, and the use of the oils and fats or triglycerides in a food, beverage or pharmaceutical composition.