The terahertz photoconductive antenna driven by femtosecond laser is a common terahertz source in terahertz time-domain spectroscopic system. Because of its omni-directional radiation mode, the main lobe of photoconductive antennas is small and its directivity is poor. The effective control of the wide-band terahertz beam is important to improve the emission efficiency of the photoconductive antennas. Using low-temperature growth gallium arsenide (LT-GaAs) as the substrate material of antenna, the electromagnetic distribution characteristics of terahertz wave radiated by the butterfly antenna are simulated by the electromagnetic software CST, and the effect of dielectric lens on terahertz wave radiated by a butterfly antenna is studied. The optimum expanding region thickness of lens is obtained by theoretical and numerical analysis. The simulation results show that with the increase of frequency, the butterfly antenna can obtain higher directivity with a thinner expanding region of the silicon lens.