Measurement of the cross-sections of 79Br(n,2n)78Br, 81Br(n,p)81mSe, 81Br(n,α)78As, and 79Br(n,α)76As reactions was carried out at specific neutron energies precisely 13.5±0.2, 14.1±0.2, 14.4±0.2, and 14.8±0.2 MeV relative to the standard 93Nb(n,2n)92mNb and 27Al(n,α)24Na reference reactions using offline γ-ray spectrometry and neutron activation. The monoenergetic neutrons were generated at the China Academy of Engineering Physics, via a 3H(d,n)4He reaction using a K-400 Neutron Generator equipped with a solid 3H-Ti based target. The activity of reaction produce was obtained utilizing a high-purity germanium detector. The cross-sections of the (n,2n), (n,p), and (n,α) reactions on the bromine isotopes were conducted in the 13–15 MeV neutron energy range. The covariance analysis approach was employed for a thorough inspection of any uncertainties within the measured cross-section data. Discussion and comparison of the observed outcome were carried out with previously published data, in particular with the results of the JENDL-4.0, JEFF-3.3, TENDL-2019, and ENDF/B-VIII.0 data libraries, along with the theoretical excitation function curve derived by employed the TALYS-1.95 program. Improved cross-section restrictions for the investigated processes in the 13–15 MeV neutron energy range will be furnished by the current findings, which will help to raise the caliber of the associated databases. Furthermore, the parameters of the pertinent nuclear reaction models can be verified using this data.