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The neutron capture cross section for the 164Dy(n,γ)165Dy reaction at 0.0372 eV energy was measured using the horizontal channel (Neutron Diffraction Facility) of Es-Salam nuclear research reactor in Birine-Algeria. The Neutron Activation Analysis (NAA) technique using 197Au(n,γ)198Au as reference reaction was adopted. The γ ray spectra for the Dy2O3 target powder and two thin gold foil were detected for the Germanium Hyper Pure coupled in the Genie 2000 data acquisition software. A resulting σ-value (2198.5 ± 94) b was measured for the thermal neutron cross section after correcting the thermal neutron self-shielding and γ attenuation effects. The measured value was then compared to the evaluated cross sections reported in two different libraries of neutron databases ENDF/B-VIII.0 and JEFF-3.3. The measured data at 0.0372 eV has been extrapolated to the energy of 0.0253 eV assuming 1/ν dependence in the thermal energy region and the result was compared with the fully measured values reported in the literature.