The invention relates to a preparation method of an epoxy succinic acid polymer with a sulfonic group. The epoxy succinic acid polymer is obtained through copolymerization of monomers of epoxy succinic acid, itaconic acid and sodium methallyl sulfonate, and the mass ratio of the monomer epoxy succinic acid to the itaconic acid to the sodium methallyl sulfonate is 2:2:1. According to the preparation method, with the epoxy succinic acid, itaconic acid and sodium methallyl sulfonate as the monomers, ammonium persulfate as an initiator and isopropanol as a chain transfer agent, polymerization of the three monomers is effectively promoted, so that the conversion rate of a polymerization reaction is high, and the obtained polymer has good scale inhibition performance, iron oxide dispersion performance and biodegradability. The ternary polymer is specially used as a dirt dispersion agent and applied to industrial circulation of cooling water and has the main advantages that the ternary polymer is free of phosphorus or nitrogen and easily biodegradable and cannot pollute the water environment after being used for a long time.