A numerical study is performed to estimate on an unsteady thermal stratification phenomenon in the Shutdown Cooling System (SCS) piping branched off the Reactor Coolant System (RCS) piping of Nuclear Power Plant. In the results, turbulent penetration reaches to the 1st isolation valve. At 500sec, the maximum temperature difference between top and bottom inner wall in piping is observed at the starting point of horizontal piping passing elbow. The temperature of coolant in the rear side of the 1st isolation valve disk is very slowly increased and the inflection point in temperature difference curve for time is observed at 2700sec. At the beginning of turbulent penetration from RCS piping, the fast inflow generates the higher temperature for the inner wall than the outer wall in the SCS piping. In the case the hot-leg injection piping and the drain piping are connected to the SCS piping, the effect of thermal stratification in the SCS piping is decreased due to an increase of heat loss compared with no connection case. The hot-leg injection piping affected by turbulent penetration from the SCS piping has a severe temperature difference that exceeds criterion temperature stated in reference. But the drain piping located in the rear compared with the hot-leg injection piping shows a tiny temperature difference. In a viewpoint of designer, for the purpose of decreasing the thermal stratification effect, it is necessary to increase the length of vertical piping in the SCS piping, and to move the position of the hot-leg injection piping backward.