In order to clarify the mechanism of frost damage for concrete materials, we investigated the state of water in a Low Heat Portland Cement (LHPC) mortar at temperatures between T = 282 K and 202 K, using quasi-elastic neutron scattering (QENS). Below the freezing point of water (i.e., T < 273 K), a broad peak for supercooled water in the LHPC mortar was clearly observed on a QENS spectrum. In addition, the supercooled water index (SCWI), which is the ratio of the signal from the supercooled water (SCW) to the signal from the free water at 282 K (FW 282K ) (i.e., SCWI = SCW / FW 282K ), was estimated for each temperature in a freeze-thaw cycle. Consequently, it was found that there is a hysteresis in the SCWI(T) curve; the amount of the supercooled water in the freeze cycle was 1.2-1.4 times larger than that in the thaw cycle at the same temperature.