A process for chemical mechanical polishing of a semiconductor substrate characterized in that a surface to be polished of said semiconductor substrate is polished under conditions of a rotation speed of a polishing table fixing a polishing pad at the range from 50 to 200 rpm and a pressing pressure of said semiconductor substrate fixed to a polishing head against said polishing pad at the range from 700 to 18,000 Pa, by using an aqueous dispersion for chemical mechanical polishing comprising (A) an abrasive and (B) at least one compound selected from the group consisting of polycarboxylic acid having a heterocycle and anhydride thereof, and said polishing pad.