Background: Radioactive substances are water chemical contaminants. In this study, the concentration of radon was measured in drinking water supplies of Taft villages (part of Dehshir-Baft fault located in central part of Iran) and also Shirkooh area with granite rocks (containing uranium). Materials and Methods: This cross sectional research was conducted in fall 2013 and winter 2014 on the sources of drinking water and also drinking water network of Taft city of Yazd province. According to the measured radon levels; the annual effective absorbed dose was also calculated. Results: Minimum and maximum levels of radon gas were related to sample number 54 (0.88 BqL^-1) and number 31 (43.01BqL^-1). Range of radon concentrations was 1.88-43.01 BqL^-1 in samples of wells in private homes, 0.88- 20.36 BqL^-1 in supplier wells of public network of drinking water, 1.23-10.29 BqL^-1 in aqueducts, 1.23-11.49 BqL^-1 in water tap connected to the public network and 12.89 BqL^-1 in one measured spring. The annual effective absorbed dose through drinking and breathing in an environment that this water is used ranged from 0.00 msv/y (sample No.54) to 0.11 msv/y (sample No.31). Conclusion: Radon concentration was lower than the limit set by the Environmental Protection Agency of United States of America, in 82% of samples. Samples with high radon concentrations were located around Shirkooh area due to the presence of granitic rocks. Dehshir and Garizat villages located through Dehshir - Baft fault and the Radon concentration of these samples was less than the permissible limit, probably due to the inactive Fault.