The object of the present invention is to provide a process for chemical mechanical polishing of semiconductor substrate that is particularly useful for chemical mechanical polishing a wafer having a wiring pattern and an insulating layer having a low dielectric constant is formed between wiring patterns, interlayers in the case of a multi-layer wiring and the like in the process of producing a semiconductor device, and an aqueous dispersion for chemical mechanical polishing which is used in this process. The process for chemical mechanical polishing of a semiconductor substrate of the present invention is that a surface to be polished of the 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 the semiconductor substrate fixed to a polishing head against a polishing pad at the range from 700 to 18,000 Pa, by using an aqueous dispersion for chemical mechanical polishing comprising an abrasive and at least one compound selected from the group consisting of polycarboxylic acid having a heterocycle and anhydride thereof, and the polishing pad.