The polyzwitterionic acid antiscalant is an antiscalant for use in desalination plants and the like for inhibiting CaSO4 and SO42− scale precipitation. The polyzwitterionic acid (PZA) antiscalant has the following structural formula: In order to make the PZA antiscalant, N-carboethoxymethyl-3-(N,N-diallylamino)propanesulfonate, a zwitterionic monomer, is cyclopolymerized in aqueous solution using tert-butyl hydroperoxide (TBHP) to make an intermediate polyzwitterion (PZ). Acidic hydrolysis of the ester groups of the PZ is performed to produce the PZA antiscalant. Evaluation of the antiscalant properties of the PZA antiscalant using concentrated brines revealed that the PZA antiscalant, at a concentration of 10 ppm, is very effective in inhibiting the formation of calcium sulfate scale, particularly in reverse osmosis plants.