A polishing composition contains at least one water soluble polymer selected from the group consisting of polyvinylpyrrolidone and poly(N-vinylformamide), and an alkali, and preferably further contains at least one of a chelating agent and an abrasive grain. The water soluble polymer preferably has a weight average molecular weight of 6,000 to 4,000,000. The polishing composition is mainly used in polishing of the surfaces of semiconductor wafers such as silicon wafers, especially used in preliminary polishing of the surfaces of such wafers.