To provide a technique employed when a plane to be polished of a silicon dioxide type material layer is polished in production of a semiconductor integrated circuit device, which is capable of polishing protruded portions by priority while suppressing polishing at recessed portions and planarizing the plane to be polished at a high level with an extremely small polishing amount, with small pattern dependence of the polishing rate. In production of a semiconductor integrated circuit device, when a plane to be polished is a plane to be polished of a silicon dioxide type material layer, a polishing compound containing cerium oxide particles, a water-soluble polyamine and water is used as a polishing compound for chemical mechanical polishing to polish the plane to be polished.