The invention provides a chemical-mechanical polishing composition including (a) an abrasive comprising alumina particles, silica particles, or a combination thereof, (b) a rate accelerator comprising a phosphonic acid, an N-heterocyclic compound, or a combination thereof, (c) a corrosion inhibitor comprising an amphoteric surfactant, a sulfonate, a phosphonate, a carboxylate, a fatty acid amino acid, an amine, an amide, or a combination thereof, (d) an oxidizing agent, and (e) an aqueous carrier. The invention also provides a method of polishing a substrate, especially a substrate comprising a cobalt layer, with the polishing composition.