Traditional concrete is effectively an insulator in the dry state. However, conductive concrete can attain relatively high conductivity by adding a certain amount of electronically conductive components in the regular concrete matrix. The main purpose of this study is to investigate the electrical and thermal properties of conductive concrete with various graphite contents, specimen dimensions and applied voltages. For this purpose, six different mixtures (the control mixtures and five conductive mixtures with steel fibers of 2% by weight of coarse aggregate and graphite as fine aggregate replacement at the levels of 0%, 5%, 10%, 15% and 20% by weight) were prepared and concrete blocks with two types of dimensions were fabricated. Four test voltage levels, 48 V, 60 V, 110 V, and 220 V, were applied for the electrical and thermal tests. Test results show that the compressive strength of specimens decreases as the amount of graphite increases in concrete. The rising applied voltage decreases electrical resistivity and increases heat of concrete. Meanwhile, higher electrical current and temperature have been obtained in small size specimens than the comparable large size specimens. From the results, it can be concluded that the graphite contents, applied voltage levels, and the specimen dimensions play important roles in electrical and thermal properties of concrete. In addition, the superior electrical and thermal properties have been obtained in the mixture adding 2% steel fibers and 10% graphite.