The invention provides a preparation method of a lactic and glycolic acid. The method comprises a catalyst containing three compounds of a catalytic induction system. The catalyst catalyzes and induces ring cleavage copolymerization between diglycolide and lactide to synthesize lactic and glycolic acid. The monomer to catalyst (mol ratio) is at 20,000 to 500,000 and the reaction temperature is 100 to 220 DEG C for 1 to 200 hours with inert gas protection or in vacuum. The invention has the advantages of high transformation ration, low catalyst contents of products, high molecular weight, narrow molecular weight disposition, good heat stability, small degradation of high temperature molten, good uniformity of materials, and is provided with excellent biological degradability and biologicalcompatibleness. The lactic and glycolic acid prepared by the invention can be widely used for surgical operation suture, internal fixation of fracture, tissue repair, plastic surgery, anti-organic conglutination, medical slow release, organic engineering, etc.