The (n,p) reaction cross sections of 16O in the neutron energy range from 13.6 to 14.9 MeV were measured by the activation method. The gamma-ray counting technique was applied, and the cross sections were determined relative to the 27Al(n,p)27Mg reaction cross sections. The neutrons were produced via the 3H(d,n)4He reaction on a SAMES T-400 neutron generator, and the induced gamma activities were measured by a high-purity germanium (HPGe) detector. The efficiency calibration of the HPGe detector for gamma-ray energies above 6 MeV was determined by means of gamma rays emitted from the decay of 11Be. An automated fast sample transport system was combined with the neutron generator in order to carry out the measurements in cyclic mode. The experimental method is described and the sources of systematic errors are discussed. The results obtained are compared with the experimental data in the available literature and recent evaluations.