The capture cross sections at stellar energies are very difficult to measure directly. Hence, data are usually evaluated by using indirect methods or extrapolations from the experimental data obtained at the lowest possible energies. The asymptotic normalization coefficient (ANC) approach of the transfer reactions provides a reliable way for the determination of the capture cross sections at stellar energies. By virtue of its reliability, we have calculated the capture cross sections of the 10Be(n,γ)11Be reaction by using nuclear ANC method. 11Be is a well-known neutron halo nucleus with two weakly bound states. As a typical example, we have shown that the radiative cross sections for a nucleon captured into a halo state are obviously enhanced. The enormous enhancement of the capture cross section is just due to the large overlap of the incident neutron wave with the extended tail of the halo. The 10Be(n,γ)11Be capture reaction is involved in the inhomogeneous big-bang nucleosynthesis. We have evaluated its reaction rates at stellar energies with the nuclear ANC method.