Abstract: The neutron capture reaction of ¹⁷⁵Lu is of great importance in nuclear reactors and heavy ion nucleosynthesis processes in the universe. The existence of a 122.8 keV isomeric state (^176mLu) in ¹⁷⁶Lu increases the difficulty in measuring the cross sections of ¹⁷⁵Lu(n, γ)¹⁷⁶Lu reaction. To study this reaction cross-section and its impact on s-process nucleosynthesis, the TALYS-2.0 program was used to calculate the total cross-section of the ¹⁷⁵Lu neutron capture reaction and the partial cross-sections for the production of the ¹⁷⁶Lu ground state and isomeric state in the energy range of 0.01~20 MeV. The results were compared with data from the EXFOR experimental database and the ENDF evaluated nuclear data library. The results show that when the nuclear level density model and the photon strength function model are optimized in combination, the calculated results are in good agreement with the experimental values. Additionally, the Maxwellian-averaged cross-sections were calculated in the energy range of 0.01~100 keV and compared with the experimental values from the KADoNiS v0.3 database. At kT=30 keV, the calculated value agrees well with the experimental value, with a relative deviation of 4.1%. This study demonstrates that the TALYS program can effectively describe the ¹⁷⁵Lu(n, γ)¹⁷⁶Lu reaction cross-section, providing a reference for further parameter optimization and validation of experimental data, which is of great significance for investigating s-process nucleosynthesis.