Search for cosmic dark matter is one of the most important tasks in both astrophysics and particle physics. Various types of highly sensitive radiation detectors have been applied to searching for dark matter in the world. The NaI(Tl) scintillator is well-known radiation detector: it has been applied to the studies of dark matter and rare processes of fundamental physics. One needs to purify the detector down to a few µBq/kg to search for dark matter because of extremely small expected event rate of dark matter candidate. The author describes the recent status of low background detectors for dark matter search and the project to search for dark matter by using highly radiopure NaI(Tl) scintillator.