The present invention provides a novel polymer, and a mixture and a cement admixture thereof. The cement admixture has higher dispersibility compared to the previous ones. The novel polymer of the present invention has a different structure from the conventional copolymers used for cement admixtures, using an unsaturated carboxylic acid monomer and an unsaturated polyalkylene glycol monomer as the monomer components.The novel polymer of the present invention basically contains a polyalkylene glycol chain and a polymer segment bonded to the chain. Another type of the novel polymer of the present invention contains two polyalkylene glycol chains and a polymer segment connecting the chains. In these polymers, at least one of unsaturated monomers constituting the polymer segment is an unsaturated carboxylic acid monomer or an unsaturated polyalkylene glycol monomer. The cement admixture of the present invention comprises a polymer, made from these monomers, or a mixture thereof.