To obtain a polishing liquid composition capable of increasing the polishing speed of a magnetic disk substrate.

This composition for polishing the magnetic disk substrate is a polishing liquid comprising water, a polishing material and a polishing accelerator and the polishing accelerator is composed of at least one kind selected from the group consisting of a divalent or more polyvalent carboxylic acid having either one of alkene group (C=C), alkyne group (C≡C), ether group (C-O-C), thioether group (C-S-C), ketone group [(C=O)] or an aromatic ring as a functional group and a salt thereof.