A procedure was developed for measuring the concentration of copper, in the Instrumental Neutron Activation Analysis method, by measuring the produced 64Cu isotope activity (after irradiation) from the annihilation peak (511-keV peak). In this procedure the number of counts under the annihilation peak is divided into two categories: (a) counts coming from the decay of the 64Cu isotope and (b) counts coming from the interactions of energetic photons (with energies >1.022 MeV, the pair production threshold) with the detector and surrounding materials. The last category is evaluated and subtracted from the annihilation peak counts, and the rest of the counts are used to calculate the activity of 64Cu. Measuring copper concentration using this method will improve its detection limit. The method was validated by measuring the concentration of copper in four International Atomic Energy Agency (IAEA) reference materials: Soil-7, Lake Sediment, Human Hair, and Hay Powder. The maximum deviation between the results and that given in IAEA certificates is 4.4%. The method decreased the detection limits of the four samples to ~3, ~4.5, ~0.6, and ~1 mg/kg, respectively.