PURPOSE: To provide the title cement hardening accelerator capable of improving the workability, strength developing property, and appearance of the hardened body by composing the accelerator out of a latent hydraulic substance, aluminum sulfate, sodium sulfate, and potassium sulfate.

CONSTITUTION: The cement hardening accelerator consists of the slag such as blast-furnace slag, activated silica, fly ash, a latent hydraulic substance (a) such as slaked lime, aluminum sulfate (b), and sodium sulfate or potassium sulfate (c). Either the anhydride or the hydrate can be used as the component (b), the grain size is preferably controlled to ≤0.5mm, especially to ≤0.25mm, and 50W500pts.wt., or preferably 100W300pts.wt., component (b) is used for 100pts.wt. component (a). Meanwhile, sodium sulfate is preferably used as the component (c) from the standpoint of workability and strength development, and 50W500pts.wt., or preferably 100W300pts.wt., component (c) is used for 100pts.wt. component (a).