Matrix inversion method is presented to unfold the gamma-ray spectrum obtained with an NaI(Tl) detector using several standard gamma-ray sources. The method is based on response matrix generated by Monte Carlo simulation of mono-energy gamma-ray photon ranging from 10 keV to 1 MeV in step of 10 keV. The comparison of the measured and simulated response function was also performed in order to validate the simulation response function. Good agreement was achieved around the photo-peak region of the spectrum, but slight deviation was observed at low energy region especially at Compton continuum region. The Compton continuum count was significantly transferred into the corresponding photo-peak and consequently the peak to background ratio was improved substantially by the application of the unfolding method. Therefore, small peak can be identified and analyzed that would otherwise be lost in the background.