In this paper, a novel method is proposed to control and reduce the side-lobe level (SLL) of the pyramidal horn antennas. In this method, graphene sheets are deposited on the antenna walls to taper the aperture field leading to pattern engineering with the goal of the side-lobe level reduction. In essence, graphene sheet acts as a high impedance surface (HIS) and hinders electromagnetic power from reaching to the horn antenna aperture edges, in such a way that the diffraction phenomenon could be drastically diminished. The proposed design is numerically analyzed and optimized using full wave 3D simulation methods. Numerical full-wave results illustrate more than 17.6 dB reduction in the side lobe level of the proposed antenna.