In this Letter, the enhanced and directional radiation in a wide terahertz (THz) frequency range in a graphene hyperbolic medium excited by an electric dipole is presented. The numerical simulations and theoretical analyses indicate that the enhanced radiation comes from the strong surface plasmon couplings in the graphene hyperbolic medium, consisting of alternative graphene and dielectric substrate layers. The simulation results also show that the peak power flow of the enhanced THz radiation in the graphene hyperbolic medium is dramatically enhanced by more than 1 order of magnitude over that in a general medium within a certain distance from the dipole, and the electromagnetic fields are strongly concentrated in a narrow angle. Also, the radiation fields can be manipulated, and the fields’ angular distributions can be tuned by adjusting the dielectric permittivity and thickness of the substrates, and the chemical potential of graphene. Accordingly, it provides a good opportunity for developing miniature, integratable, high-power-density, and tunable radiation sources in the THz band at room temperature.