As the nuclear radiation has started to be used in a variety of different fields, it is important to be protected from it, and thus the radiation measurement becomes vital. The quality of the performance of a detection system, used for the energy measurements, is important. It is characterized by the width of the pulse-height distribution, obtained for the particles of the same energy (monoenergetic source). The energy spectrum of a radiation source depends on the type and energy of the incident particle and the type of the detector. In this work the energy resolution of a 3 '' x 3 '' NaI(Tl) detector has been measured for photon energies of 511, 662, 835, 1173, 1275, and 1332 keV, and its variation with the detector-source distance was investigated. The energy resolution of a detector system is obtained from the peak full width at one-half of the maximum height (FWHM) of a single peak (for a particular energy) as a function of detector-source distance. It was found that the energy resolution has decreased with the increasing distance.