We present a study for a THz receiver based on graphene. First, the dipole and the bowtie THz antennas on graphene are designed, and followed by the on-wafer fabrication of a graphene diode matched to the antenna. Finally the responsivity of the receiver up to 10 THz is computed. Our results show that the antenna and the diode behaviors exhibit new properties (e.g., the antennas are acting as high reactive impedance surfaces, the diode is rectifying only due to its geometrical shape). These new properties are due to the physical properties of graphene having the carrier transport described by Dirac equation.