With abundances and 2σ upper limits of fluorine (F) in seven metal-poor field giants, nucleosynthesis of stellar F at low metallicity is discussed. The measurements are derived from the HF(1-0) R9 line at 23358 Å using nearinfrared K-band high-resolution spectra obtained with CRIRES at the Very Large Telescope. The sample reaches lower metallicities than previous studies on F of field giants, ranging from [Fe/H] = −1.56 down to −2.13. Effects of three-dimensional model atmospheres on the derived F and O abundances are quantitatively estimated and shown to be insignificant for the program stars. The observed F yield in the form of [F/O] is compared with two sets of Galactic chemical evolution models, which quantitatively demonstrate the contribution of Type II supernova (SN II) ν-process and asymptotic giant branch/Wolf-Rayet stars. It is found that at this low-metallicity region, models cannot well predict the observed distribution of [F/O], while the observations are better fit by models considering an SN II ν-process with a neutrino energy of E ν = 3 × 10 53 erg. Our sample contains HD 110281, a retrograde orbiting low-α halo star, showing a similar F evolution as globular clusters. This supports the theory that such halo stars are possibly accreted from dwarf galaxy progenitors of globular clusters in the halo.