The present invention provides a multi-branched polyalkylene glycol polymer useful for various applications, especially for an admixture for cement, a dispersant, admixture for cement, and cement composition each comprising the same, a thiol compound having a polyalkylene glycol chain useful for materials and the like of the polymer, and a method for easily and effectively producing the multi-branched polyalkylene glycol polymer and the thiol compound having a polyalkylene glycol chain at low cost. The multi-branched polymer comprises: a polyalkylene glycol chain; a residue of a compound having three or more active hydrogen atoms; and a polymer portion having a constitutional unit derived from a vinyl monomer component, one end of the polyalkylene glycol chain bonding to the residue, and a terminal oxygen atom of at least one of the other ends of the polyalkylene glycol chain bonding to a main chain end of the polymer portion directly or via an organic residue.