NOVELTY - Solid acid catalyst, where the catalyst is zirconium sulfate nanoparticles of 30-900 nm grain diameter, and prepared by e.g. dissolving zirconium oxychloride octahydrate in water, stirring, adding aqueous ammonia to obtain zirconium hydroxide white precipitate, filtering, washing filtrate with water, drying and grinding into powder, dissolving polyethylene pyrrolidone in ethylene glycol, stirring, adding zirconium hydroxide white precipitate powder, transferring to polymerization kettle, then placing in an oven, setting oven at 180 degrees C for 12 hours, filtering and drying., is claimed.    USE - The catalyst is useful in the reaction of free fatty acids for preparing biodiesel (claimed).    ADVANTAGE - The catalyst: is non-corrosive, environmentally friendly and required in small dosage; can improve the conversion rate of fatty acid and can be easily separated from the product; and has high catalytic efficiency and produces less byproducts.    DETAILED DESCRIPTION - Solid acid catalyst, where the catalyst is zirconium sulfate nanoparticles of 30-900 nm grain diameter, and prepared by: (a) dissolving 5 g zirconium oxychloride octahydrate in 100 ml water, then stirring at normal temperature to form a clear solution, adding 25% aqueous ammonia, adjusting the pH value of the solution to 8 to obtain zirconium hydroxide white precipitate, filtering, washing the filtrate with water until the filtrate does not contains chloride ions, drying at 80 degrees C for 24 hours, and grinding into powder for future use; (b) dissolving 2 g polyethylene pyrrolidone in 40 ml ethylene glycol, stirring at 60 degrees C to form a clear solution, adding 0.5-4 g ground zirconium hydroxide white precipitate powder obtained in the step (a), stirring for 2 hours, adding 3 ml 2 M sulfuric acid solution, stirring for 12 hours, transferring to a polymerization kettle, then placing in an oven, setting the temperature of the oven at 180 degrees C for 12 hours, cooling to room temperature and filtering, washing and drying to obtain the nano-zirconium sulfate raw powder; and (c) roasting nano-zirconium sulfate raw powder in a muffle furnace, heating at the speed of 1 degrees C/minute to 650 degrees C constant temperature for 5 hours, is claimed. An INDEPENDENT CLAIM is also included for use of the solid acid catalyst in the reaction of free fatty acids for preparing biodiesel, comprising adding the solid acid catalyst zirconium sulfate and free fatty acid and low-carbon alcohol as a raw material into an oil bath, where the molar ratio of free fatty acid and low-carbon alcohol is 1:20-1:100 and the weight ratio of the solid acid catalyst and free fatty acid is 0.05-0.3, heating to 85-120 degrees C, reacting for 6 hours, cooling to room temperature, filtering to remove the catalyst and obtain crude product biodiesel, drying, washing with water, and then vacuum distilling to remove low-carbon alcohol and obtain the product.