We report on a study of the room-temperature nonlinear charge transport properties of three-terminal junction devices made from graphene. We demonstrate that the graphene three terminal junction devices show a rectification characteristic, namely, when voltages VL = V and VR = -V are applied to the left and the right terminal in a push-pull configuration, the voltage output from the central terminal VC is finite and is scaled approximately with V(2). The rectification coefficient can be effectively tuned by a gate voltage and shows a transport carrier polarity dependence. We further show that the nonlinear charge transport characteristics can be used to probe the electronic structure of graphene nanostructures and to study the thermoelectrical power of graphene. These results show that the graphene three-terminal junction devices could be used as novel building blocks for nanoelectronics and as novel devices for the study of the material properties of graphene on the nanoscale.