To provide a substance capable of imparting an excellent crystallization-accelerating effect to an oil or fat, and an oil or fat composition containing said substance. The oil or fat composition has an excellent crystallization-accelerating effect, and therefore can improve workability/processability and texture, such as the sugar dissolution, stickiness and texture of a fried doughnut, the filled state and hardness of shortening/margarine, and the time required for drying a coating chocolate. [Solution] The present invention is a crystallization accelerator comprising a polymer compound that includes, as constituent components, a C18-28 hydroxy saturated fatty acid, which respectively has a hydroxyl group and a carboxyl group at both terminals and may have one carbonyl group in the chain thereof, a glycerin and optionally a fatty acid, said polymer compound being obtained by polymerizing the constituent components to a molecular weight of 3,000 to 100,000.
