Abstract: Re and Re-Mo alloys are important structural materials in the space reactor study due to the characteristics of the small thermostriction, high melting point and so on. The exact neutron radiation capture reaction cross sections of the rhenium isotopes are of great significance in the space reactor design. However, in the space reactor simulation by Monte Carlo method, it was found that the k_eff values of the space reactor will have a great difference when different database was referenced. So, the existing database cannot meet the requirements of the space reactor research and high-precision experimental data are needed. In this work, the neutron radiation capture reaction cross sections of ¹⁸⁵Re and ¹⁸⁷Re, two natural isotopes of rhenium, were measured at the back-streaming white neutron source (Back-n) of the China Spallation Neutron Source (CSNS), by using the gamma total absorption facility (GTAF) and prompt gamma ray measurement method. The experiment was carried out at the second experiment station of the Back-n neutron source, and the data were measured by the digital waveshape acquiring technique based on flash analog-to-digital converter (FADC) cards. The neutron energy was determined by the time-of-flight method, and the proton pulse T₀ signal was used as the start signal. To suppress the accidental coincident backgrounds, the parameter that the detector multiplicity greater than or equal to 2 was applied, means that within the preset time window the signal amplitude of two or more channels exceeded the threshold. In the off-line data processing the interference of α-particles which caused by the radium impurity in the BaF₂ crystal were reduced by particle discrimination based on digital waveshape identification. The total energy spectrum of the γ ray cascades, radiated by the decay of the excited compound nucleus that produced in (n, γ) reactions, was reestablished by summarizing pulse’s energies of all the bombarded detectors. By the total energy spectrum analyzing, the counts of (n, γ) reaction events occurred in the sample were obtained and the backgrounds of the sample scattered neutrons were suppressed, attributed to the binding energy variance between the nuclide of the sample and the BaF₂ crystal. The experimental curves of the ¹⁸⁵Re(n, γ)¹⁸⁶Re and ¹⁸⁷Re(n, γ)¹⁸⁸Re reactions within the energy range of 0.5 eV-10 keV were obtained by relative method, and the ¹⁹⁷Au(n, γ)¹⁹⁸Au reaction was used as the standard. The comparison between the measured curves and the evaluation curves from the ENDF/B-Ⅷ.0 database were conducted. It is found that in the distinguishable resonance energy range, the experimental data and the evaluation curves were consistent with each other. The result of this work would support the space reactor physics research and can also provide technique for the neutron radiation capture cross section measurements of some other micro or radioa ctivity samples.