An admixture for cement compositions is prepared by calcining at 630.degree. to 870.degree. C. at least one substance selected from the group consisting of natural kaolin, halloysite and synthetic kaolin, effecting classification so that amorphous portions of alumina/silica having a mixing ratio of 0.5 to 1.3 form main components, with all particles having diameters up to 8 .mu.m and an average diameter of 0.5 to 2 .mu.m, and a specific gravity ranging from 2.45 to 2.55. This admixture is used to produce a cement composition such as mortar or concrete, which realizes excellent fluidity to promote workability, and a high strength structure.