This invention provides a polishing medium for chemical-mechanical polishing, comprising an oxidizing agent for a conductor, a protective-film-forming agent for protecting a metal surface, an acid, and. water; (1) the polishing medium having a pH of 3 or less, and the oxidizing agent being in a concentration of from 0.01 to 3% by weight, or (2) the polishing medium containing abrasive grains having an average particle diameter of 50 nm or less, and the abrasive grains having standard deviation of particle size distribution in a value of more than 5 nm.