A cement admixture and a cement composition having a carbonation suppressing effect and a heat-of-hydration suppressing effect are provided. A cement admixture containing one or more non-hydraulic compounds selected from the group consisting of .gamma.-2CaO.SiO.sub.2, .alpha.-CaO.SiO.sub.2 and calcium magnesium silicate, a cement composition containing said admixture, and a carbonation suppressing method by use of said cement admixture or cement composition. According to the present invention, a remarkable carbonation suppressing effect can be obtained particularly when used in portland blast-furnace slag cement. This leads to an effective use of steelmaking slag and the like, and the load of clinker can be reduced, so that a cement composition of a low environmental load type can be attained. Further, this is suitable for cements in conformity with the EN standards, which are used in civil engineering and building industries.