New experimental cross-section data for the 180W(n,2n)179mW, 186W(n,2n)185mW and 186W(n,p)186Ta reactions at the neutron energies of 13.5 and 14.4 MeV are obtained by the activation technique. The neutron beams are produced by means of the 3H(d,n)4He reaction. The gamma activities of the product nuclei are measured by a high-resolution gamma-ray spectrometer with a coaxial high-purity germanium detector. The neutron fluence is determined using the monitor reaction 93Nb(n,2n)92mNb. The results in the current work are discussed and compared with the measurement results found in the literature. It is shown that these higher accuracy experimental cross-section data around the neutron energy of 14 MeV agree with some previous experimental values from the literature within experimental uncertainties.