A process for producing an acid-type maleic acid polymer having a number-average molecular weight of 300-5000 and a D-value (defined below) smaller than 2.0, said process comprising polymerizing a monomer component composed of maleic acid (A) alone or a monomer component composed of 50-99.9 wt % maleic acid (A) and 50-0.1 wt % other water-soluble unsaturated monomer (B), without neutralization, using water as the polymerization solvent, in the presence of at least one metal ion selected from the group consisting of iron ion, vanadium atom-containing ion, and copper ion in an amount of 0.5-500 ppm of said monomer component, by the aid of hydrogen peroxide as the polymerization catalyst in an amount of 8-100 g per mol of said monomer,
- D-value=M.sub.W /M.sub.N
- M.sub.W =weight-average molecular weight
- M.sub.N =number-average molecular weight.