This paper describes the liquid scintillator veto system for the COSINE-100 dark matter experiment and its performance. The COSINE-100 detector consists of eight NaI(Tl) crystals immersed in 2200~L of linear alkylbenzene-based liquid scintillator. The liquid scintillator tags between 65 and 75% of the internal $^{40}$K background in the 2--6 keV energy region. We also describe the background model for the liquid scintillator, which is primarily used to assess its energy calibration and threshold.