High efficient coupling of graphene surface plasmons to far field radiation is possible by some techniques and can be used in the radiating applications. Besides of the coupling efficiency, the angular distribution of the radiated power is an important parameter in the radiating devices performance. In this paper we investigate the gain of the far field radiation related to the coupling of graphene surface plasmons via a high permittivity medium located close to the graphene. Our results show that high directive radiation and high coupling efficiency can be obtained by this technique and gain and directivity of radiation can be modified by graphene characteristics such as chemical potential and also quality of the graphene. Raising the chemical potential of graphene leads to increase the gain of the radiation as the result of amplifying the directivity of the radiation. Furthermore, high values of relaxation time lead to high directive and strong coupling which raises the maximum value of gain in efficient coupling angle. Tunable characteristics of gain and directivity in this structure can be important designing reconfigurable THz radiating devices.