The single crystals of triphenylphosphinselenid [C18H15PSe] were produced by slow evaporation of concentrated ethyl acetate solutions. These single crystals were exposed to Co-60 gamma (gamma) rays with a dose speed of 0.980kGy/h at the room temperature for 72h. The free radical over the sample was observed using electron paramagnetic resonance (EPR)-X band spectrometer. The EPR spectra were recorded between 120 and 400K. Furthermore, the sample irradiated was rotated in steps of 10 degrees and analyzed for different orientations of the crystal in the magnetic field. Only one radical structure was determined on the molecule. The hyperfine constants of the sample were found to be anisotropic. The average values of these constants and value of g were calculated as following: g=2.007656, a(Se)=37.47G, a(P)=27.44G, a(Ha)=17.28G, and a(Hb)=18.16G.