Within the framework of the modified potential cluster model with forbidden states and their classification according to Young diagrams, the possibility of describing experimental data on the total cross sections of the neutron radiative capture on 7Li is considered. It is shown that the model used and the methods for constructing potentials make it possible to correctly describe the behavior of experimental cross sections at energies of 1 meV to 1.5 MeV, where experimental data are available. Based on the calculated total cross sections up to 5 MeV, the reaction rate is calculated and its analytical approximation is carried out. Resonance structure of 7Li(n, γ)8Li cross section and its impact on the reaction rate is examined. It is shown that the 7Li(n, γ)8Li reaction dominates at T 9 < 0.1 as opposed to the burning of 7Li in the 7Li(3H, n)9Be and 7Li(4Нe, γ)11B reactions, but comparable to (d, γ), (d, p), and (p, γ) at T 9 ∼ 1.