<p>There is provided a cement dispersing agent and a concrete admixture which have good influence on workability (such as little setting retardation and low concrete viscosity), and are excellent in slump-loss reduction. The cement dispersing agent agent comprises an alkylene oxide modified water-soluble polymer having a structure composed of: a polymer skeleton containing a water-soluble polycarboxylic acid polymer grafted and/or crosslinked with a compound having amino and imino groups and/or a compound having amino, imino and amido groups; and an alkylene oxide that is further added to the polymer skeleton, and the concrete admixture comprises the cement dispersing agent and other admixture.</p>