There are disclosed a novel sulfur-containing poly(unsaturated carboxylic acid) and its uses and production process. A sulfur-containing poly(unsaturated carboxylic acid) having a weight-average molecular weight (Mw) of 500 to 4,500 and a molecular weight distribution (Mw/Mn) of not more than 2.5 is obtained by a production process comprising the step of polymerizing an unsaturated carboxylic acid in the presence of a polymerization initiator to thereby obtain the poly(unsaturated carboxylic acid), wherein: a combination of a persulfate and a bisulfite is used as the polymerization initiator, wherein the polymerization initiator is adjusted in such a manner that: the total amount of the polymerization initiator as used is not smaller than 10 g equivalents per 1 mol of the unsaturated carboxylic acid as used, and the amount of the bisulfite accounts for not smaller than 8 g equivalents of the total amount of the polymerization initiator as used; and the polymerization temperature is controlled so as to be in the range of 25 to 99.degree. C. This polymer is used as an essential component of a detergent builder and a kaolin dispersant.