An ultra high-strength hydraulic cement composition contains a binder, fine aggregates, coarse aggregates, an antifoaming agent, water and a specified admixture and has a unit amount of the binder in the range of 480-1800kg/m3. Water and the binder are contained at a ratio of 10-25% and the admixture is contained in the amount of 0.2-3.5 weight parts per 100 weight parts of the binder. The binder may be cement or a mixture of cement and a microscopic powder admixture. The admixture is one or more selected from reaction mixtures obtained by specified two processes and partially or completely neutralized substances obtained from such a reaction mixture through these two processes and also a specified third process. The specified two processes include initiating a radical copolymerization process of a radical polymerizable monomer mixture containing maleic anhydride and a monomer of a specified kind in a non-aqueous system in the presence of a non-aqueous radical initiator and stopping the radical copolymerization reaction in its midst while the inversion rate of polymerization is at a specified level by adding water to the reaction system to thereby obtain a reaction mixture. The specified third process is for partially or completely neutralizing the reaction mixture.