An ethoxylated pentaerythritol core hyperbranched polymer with dithiocarboxylate as side group and terminal group and its applications as a heavy metal chelating agent are disclosed, which relates to the field of chemical and environmental protection technology. The hyperbranched polymer has a chemical formula of C[CH2OCH2CH2OCOCH2CH2N(CSSM)CH2CH2NHCSSM]4, wherein M is Na+, K+ or NH4+. A preparation method of the hyperbranched polymer is simple, the raw materials are easily available, and it is easy to be industrialized. The hyperbranched polymer is able to be used as a heavy metal chelating agent. Its special three-dimensional space structure is able to alternately chelate with heavy metals to form a large three-dimensional molecular conjugate with low solubility, strong stability, and compactness, which is able to effectively treat wastewater and waste containing heavy metals.