To obtain an inorganic powder having the controlled solubility of calcium ions and aluminum ions in water by including a calcium compound and an aluminum compound containing water of crystallization at a specific molar ratio therein.

This inorganic powder is obtained by compounding a calcium compound selected from calcium hydroxide, calcium oxide, calcium nitrate, calcium silicate and calcium chloride with an aluminum compound, selected from aluminum hydroxide, kaolinite, montmorillonite, halloysite, gibbsite and pyrophyllite and containing water of crystallization in which ≥5 wt.% thereof is dehydrated in a temperature region of 20-200°C so as to provide 0.1-10 molar ratio of the aluminum/calcium. The inorganic powder in an amount of 1-100 pts.wt., preferably 3-50 pts.wt. is added to 100 pts.wt. cement to afford a cement composition. Thereby, the resultant cement composition is excellent in aggregation rate and hardening rate and the durability and dimensional stability of the resultant cement hardened material can be improved.