The nuclear resonance parameters and the capture cross section of the neutron magic isotope La-139 have been measured relative to Au-197 in the energy range of 0.6 eV to 9 keV at the neutron time-of-flight (n_TOF) facility at CERN. We describe the experimental apparatus and the data analysis procedures, which concerned mainly the efficiency correction by means of the pulse height weighting function technique and the determination of different background components. We extracted the resonance parameters and the main nuclear quantities such as the resonance integral RI=10.8 +/- 1.0b, the average gamma widths for s and p waves (l=0)=50.7 +/- 5.4 meV and (l=1)=33.6 +/- 6.9 meV, the nuclear level densities < D >(l=0)=252 +/- 22 eV and < D >(l=1)< 250 eV, and the neutron strength functions S-0=(0.82 +/- 0.05)x10(-4) and S-1=(0.55 +/- 0.04)x10(-4). These results represent a significant improvement over previous data. The deduced Maxwellian-averaged capture cross sections are important for the interpretation of the most recent spectroscopic observations in low-metallicity stars.