A polishing composition for memory hard discs used to obtain polished surfaces of a high precision and a high quality with a high stock removal rate. The composition consists of water, alumina polishing agent, and polishing accelerator, and polishes surfaces of alumite, aluminum, and non-electrolytically nickel plated memory hard discs. The polishing accelerator is one kind selected from the group of molybdate of ammonium molybdate, lithium molybdate, sodium molybdate and potassium molybdate, or a kind selected from the group of molybdate and aluminum salt such as aluminum nitrate or aluminum oxalate, or another one kind selected from the group of molybdate and nickel sulfate, nickel nitrate, nickel sulfamate, and nickel acetate. The addition quantity of the substance above is 0.1 to 20%, the weight ratio of the polishing agent is 2 to 30%, and the mean particle diameter is 0.3 to 10 .mu.m.