The neutron capture cross section of the neutron magic isotope 139La has been measured relative to that of 27Al by means of the activation method. The fast neutrons were produced via the 3H(d,n)4He reaction on Pd-300 neutron generator. The natural high-purity La2O3 powder was used as target material. Induced gamma activities were measured by a high-resolution gamma-ray spectrometer with high-purity germanium (HPGe) detector. Measurements were corrected for gamma-ray attenuations, random coincidence (pile-up), dead time and fluctuation of neutron flux. The new values for En=13.5±0.2, 14.1±0.2, and 14.8±0.2MeV are found to be 1.30±0.08, 1.15±0.08 and 0.99±0.07mb, respectively. Results were discussed and compared with some corresponding values found in the literature.