The invention discloses a ZrO2 polycrystal foamed ceramic catalyst comprising elements Zr, Al and Ti which are in the molar ratio of 5:(2.2-3.5):0.2. The invention further discloses a preparation method of the ZrO2 polycrystal foamed ceramic catalyst, and ZrOCl2.8H2O, AlCl3 and TiCl4 are utilized to take part in a reaction. The invention further discloses an application of the ZrO2 polycrystal foamed ceramic catalyst, the ZrO2 polycrystal foamed ceramic catalyst is used for catalyzing glycerin esterification to reduce the acid value of biodiesel, and an esterification reaction is carried out by taking the biodiesel as a reaction raw material, ZrO2 polycrystal foamed ceramic as the catalyst and glycerin serving as a byproduct of the biodiesel as an esterifying agent. The ZrO2 polycrystal foamed ceramic catalyst is efficient, clean, green and environment-friendly, and free fatty acid in the biodiesel is converted into fatty glyceride by the esterification reaction of the fatty acid and glycerin serving as the byproduct of the biodiesel, so that the aim of reducing the acid value is achieved.