It is very important to consider the amount of UV (ultra-violet) radiation for life existence and evolution becausemoderate UV radiation is necessary for the synthesis of biological compounds. Recently, life on the low mass stars hasbeen suggested because of their long lifespan. However, these stars are out of ‘‘common region’’ between HZ (habitablezone) and UV-HZ, where the persistent life existence is expected because of lack of UV radiation. Then, this paperconsiders UV-HZ with the intensive supply of UV radiation from Coronal Mass Ejection (CME) and explores to increasethe range of the common region around low mass stars. Then, we find the common region doesn’t always spread so muchbecause CME size is proportion to the distance from a host star and the peak of UV luminosity depends on evolutionaryphase of main sequence stars.