Granite is one of the rock under igneous rock. Granites are the result of rapidly injected coalescing sheet of magma. Concerning their compositions, granitic rocks mainly consist of coarse grains of quartz, K-feldspar and plagioclase. Mafic common minerals in granites include biotite and amphibole. Zircon, sphene, apatite and allanite are other common accessory minerals in granites. Granites are widely used as building and ornamental materials, including indoor covering. In this thesis the activity concentration of 226Ra, 232Th, 40K, 235U and 137Cs in 18 plutonic rock samples were investigated. Fifteen rock samples were collected from the surface of locations and three rock samples from outcrops. These samples were collected randomly according to color and texture of the rocks from 3 three different regions Ganjnameh. Darreh Morad Beig and Tarik darreh from Alvand plutonic complex in Hamedan. Collected samples have been miled and passed from mesh no50 changing into fine powder in the laboratory. The prepared powder packed in Negin standard container and sealed. Gamma ray spectrometry was done using HPGe detector setup, coaxial p type with 38.5% relative efficiency and 4096 channel MCA. In this work, determined specific activity in Bq/kg for some kind of stones. The activity concentration of 226Ra, 232Th and 40K in samples varied from 9.54±0.86 up 119.27±1.86, 10.48±1.19 up 268.41±3.27 and 88.97±3.34 to 1602.58±27.93 Bq/kg, respectively. The highest activity concentration of 226Ra and 232Th were found in pegmatite sample from the Ganjnameh region while the most value for 40K observed in Syenogranite garnet bearig sample at the same local in Ganjnameh. The activity concentration of 235U and 137Cs varied from 0 to 11.34±3.48 Bq/kg and 0 to 4.86±0.66 Bq/kg, respectively. Thin sections for mineralogical study of the rock samples were prepared and were investigated using polarizing microscope to define mineralogical composition of the platonic rock samples. The results of