The present invention has for its object to provide an economical cement additive capable of reducing the amount of water to be added to cement compositions and still capable of providing cement compositions with high fluidity, good processability, and a proper level of air-entraining ability resulting from sufficient foaming prevention, at low addition levels, a cement composition in which the above cement additive is used, and a polycarboxylic acid polymer excellent in dispersing effects on cement particles or inorganic powders or pigments and capable of being used with advantage as a cement additive or a dispersant for various uses.The invention provides, among others, a cement additive comprising, as main component, a polycarboxylic acid polymer (X) which has; repeating units (A), (B), (C) and (D), wherein none of the proportion of occurrence S1 of repeating unit (A) the proportion of occurrence T1 of repeating unit (B) and the proportion of occurrence E1 of repeating unit (C) is not equal to zero, the average number n of moles of an oxyalkylene group as added in repeating unit (B) is not less than 110, and that the weight average molecular weight of said polycarboxylic acid polymer is not less than 10000.