A method for the preparation of polyol from an unsaturated TAG oil that can function similarly to castor oil in certain applications. The method comprises controlled epoxidation of the TAG oil with an acid and an oxidizing agent to obtain a partially epoxidized TAG oil with desired iodine and oxirane values; hydroxylating the partially epoxidized TAG oil using a monoalcohol and a solid acid catalyst to obtain the polyol. The resulting polyols are comprised of a triglyceride structure and hydroxyl values, viscosities, and colors that are similar to castor oil.