Within the framework of the modified potential cluster model with a classification of orbital states according to Young diagrams, the possibility of describing experimental data for total cross sections of the neutron radiative capture on 11B to the ground state of 12B at energies of 10 meV (1 meV = 10−3 eV) to 7 MeV was considered. It was shown that, taking into account only the E1 transition from the S state of the n11B scattering to the ground state of 12B, it is quite possible to explain the magnitude of the known experimental cross sections at energies of 25.3 meV to 70 keV. Furthermore, on the basis of the total cross sections of 10 meV to 7 MeV, but excluding resonances above 5 MeV, the reaction rate is calculated in the temperature range of 0.01 to 10.0 T9. It is shown that the inclusion of low-lying resonance states makes a significant contribution to the reaction rate, starting already with temperatures of 0.2–0.3 T9.