The present invention was made in view of the above state of the art, and has an object to provide a polycarboxylic acid polymer for a cement admixture which has a novel polymer structure and can provide a cement composition superior in workability without increasing an amount of the polycarboxylic acid polymer for a cement admixture to be added to cement and in addition can impart adequate workability to a cement composition having a relatively small slump value, a cement admixture comprising the polycarboxylic acid polymer for a cement admixture, a cement composition comprising the cement admixture and cement and a method of producing the polycarboxylic acid polymer for a cement admixture. The present inventors found that a polycarboxylic acid polymer for a cement admixture having a branched structure on the main chain, the side chain of which is a polyalkylene glycol chain having 2 to 18 carbon atoms, can provide a cement composition superior in work ability without increasing an amount of the polycarboxylic acid polymer for a cement admixture to be added to cement and in addition can impart adequate workability to a cement composition having a relatively small slump flow value.