Within the framework of the modified potential cluster model with forbidden states, the total cross-sections of radiative n
9Be capture to the ground and five low-lying excited states are calculated at energies from 10-2 eV up to 5 MeV. The thermal cross-section σ
th
= 8.35 mb is in good agreement with experimental data. We included in the consideration five resonances at the excitation energy Ex
from 7.371 MeV up to 10.570 MeV and corresponding to the following states with J
π (Ex
, MeV): 3- (7.371), 2+ (7.542), 3+ (9.4), 2+ (9.56), and 3- (10.570). The partial and total 9Be(n,γ0+1+2+3+4+5)10Be reaction rates are calculated at temperatures from 0.001 to 10 T
9. Contrary to the available data, we propose the rising of reaction rate near factor five at T
9 >1 is mainly due to the first 3- (0.559 MeV) resonance. We foresee this contrast is coming from the different model approaches.