Recent development in Terahertz (THz) and millimeter technology shows that the decent advantages of THz radiation over old technologies of X-Ray and microwaves have made it as a promising method for imaging applications. The THz frequency band offers several advantages over microwave links as well as free-space infrared IR based systems, such as higher bandwidth capacity and spatial resolution, perforation capability, lower photoionization effects on biological tissues, and still unregulated. To be used as an imaging appliance, a THz source must meet feasible requirements such as high gain, narrow beamwidth, and proper side lobe level (SLL) from its radiation pattern, to produce a high-resolution spectra output by raster scanning technique with a focused THz beam. A high radiation efficiency also needs to be dealt with, because it will affect the amount of energy by an antenna can radiate. In the previous research, we have studied a bow-tie planar antenna combined with a capacitive bar on a high-dielectric Silicon substrate and extended hemispherical lens to obtain a 1 THz resonant frequency, gain of more than 30 dB and radiation efficiency of 69.3%. However, the design has a drawback of high SLL which can affect the image detection. A modification is needed for the bow-tie antenna to suppress the SLL in an acceptable level. In this paper, we study the modification of the bow-tie antenna with a double cross technique. Two bow-tie antennas are cross designed for each other with different arm length. Two-cross dipole design has obtained an isotropic radiation pattern of a single antenna. We adopt this technique to be implemented on a lens-based antenna for SLL suppression. From the simulation results, the high gain and radiation efficiency performances are conformable to our previous study, but lower SLL can be achieved as well. The SLL can be reduced to -11.3dB and -11.7dB for both E-plane and H-plane of the radiated waves. These results indicate that our proposed design has great advantages to be used for future imaging applications.