The ²³⁸U(n, γ)²³⁹U reaction cross-section at average neutron energy of 3.7 ± 0.3 MeV from the ⁷Li(p, n)7Be reaction has been determined using activation and off-line c-ray spectrometric technique. The ²³⁸U(n, γ)²³⁹U and ²³⁸U(n, 2n)²³⁷U reaction cross-sections at average neutron energy of 9.85 ± 0.38 MeV from the same 7Li(p, n)7Be reaction have been also determined using the above technique. The experimentally determined ²³⁸U(n, γ)²³⁹U and ²³⁸U(n, 2n)²³⁷U reaction cross-sections were compared with the evaluated data of ENDF/B-VII, JENDL-4.0, JEFF- 3.1 and CENDL-3.1. The experimental values were found to be in general agreement with the evaluated value based on ENDF/B-VII, and JENDL-4.0 but not with the JEFF-3.1 and CENDL-3.1. The present data along with literature data in a wide range of neutron energies were interpreted in terms of competition between different reaction channels including fission. The ²³⁸U(n, γ)²³⁹U and ²³⁸U(n, 2n)²³⁷U reaction cross-sections were also calculated theoretically using the TALYS 1.2 computer code and were also found to be in agreement experimental data.