The cross-sections of the \(^{113,115}\) In(n, \(\gamma\) ) reactions play critical roles in s-process nucleosynthesis and neutron resonance capture analysis for determining the elemental and isotopic composition of archeological and cultural heritage, and Ag–In–Cd control rods in commercial nuclear reactors. The neutron capture cross-sections of indium from 1 eV to 1 MeV were measured at the Back-n facility of the Chinese Spallation Neutron Source (CSNS) using the time-of-flight (TOF) method. In the resolved resonance region, the resonance parameters of \(^{113,115}\) In were extracted using the R-matrix code SAMMY from 1 eV to 2 keV. The inconsistencies between the available experimental data and the evaluated libraries were analyzed. In the unresolved resonance region, astrophysical Maxwellian-averaged cross-sections (MACSs) of the \(^{113,115}\) In(n, \(\gamma\) ) reactions were calculated over the temperature range relevant to s-process nucleosynthesis, based on the present averaged cross-sections. At a typical s-process temperature of \(kT=30\) keV, the MACS of \(^{115}\) In(n, \(\gamma\) ) is about 20% higher than the recommended value of KADoNiS v0.3, while showing better agreement with KADoNiS v1.0.