Chemical mechanical polishing (CMP) compositions, methods and systems for polishing cobalt or cobalt-containing substrates are provided. Dual, or at least two chelators are used in the CMP polishing compositions as complexing agents for achieving the unique synergetic effects to afford high, tunable Co removal rates, and low static etch rates on Co film surface for efficient Co corrosion protection during CMP process. The cobalt chemical mechanical polishing compositions also provide very high selectivity for Co film removal vs. removal of other barrier layers, such as Ta, TaN, Ti, and TiN, and dielectric film, such as TEOS, SiNx, low-k, and ultra low-k films.