In this work a novel design of an ultra-wideband and highly directive Vivaldi photoconductive antenna (PCA) is reported for the first time for the THz sensing and imaging applications. The optical-to-THz conversion efficiency for the enhanced directivity of the reported PCA is enhanced by adding a hemispherical silicon-based lens with the PCA gold electrode and quartz substrate (Epsilon r = 3.78, tan delta = 0.0001). The optimization of the antenna design parameters is performed in CST MWS for the frequency range of 1-6 THz. The design antenna has UWB -10 dB impedance and 3-dB AR bandwidths of 6 THz, maximum directivity of 10 dBi and maximum total radiation efficiency of > 40%.