Terahertz (THz) technology has become an interest research topic in the last decade due to its radiation performance advantages. However, the high atmospheric attenuation of THz wave spectrum remains one of the issues that are necessary to be considered to provide acceptable performance for practical applications. Effective energy transfer from electrical signals into electromagnetic waves and a high gain antenna performance are two conditions that are useful for tackling that issue. Another parameter of sidelobe level (SLL) is also essential to be suppressed to provide the high directive antenna. This paper proposes an optimum matching layer design on an extended hemispherical Silicon lens fed with a THz double crossed bow-tie antenna to enhance radiation performance, i.e., gain, beamwidth, and side lobe level to provide a high radiation performance antenna design for a THz system. From simulation results by using CST Microwave Studio, the obtained gain and radiation efficiency at optimal condition are 34.07 dB and 82.88%, respectively. The SLL and beamwidth respectively show better performances at equally around -12 dB and 2.4° for both E-Plane and H-plane. Those results show that the proposed design antenna can provide high radiation performance for THz applications that need high gain antenna radiation performance.