We report the performance of an active veto system using a liquid scintillator with NaI(Tl) crystals for use in a dark matter search experiment. When a NaI(Tl) crystal is immersed in the prototype detector, the detector tags 48% of the internal 40 K background in the 0-10 keV energy region. We also determined the tagging efficiency for events at 6-20 keV as 26.5 ± 1.7% of the total events, which corresponds to 0.76 ± 0.04 events/keV/kg/day. According to a simulation, approximately 60% of the background events from U, Th, and K radioisotopes in photomultiplier tubes are tagged at energies of 0-10 keV. Full shielding with a 40-cm-thick liquid scintillator can increase the tagging efficiency for both the internal 40 K and external background to approximately 80%.