Terahertz antenna is the key component of terahertz detector. The terahertz antenna can assist detectors to detect terahertz signal more efficiently. In this paper, the point effect of fractal butterfly antenna is deeply studied and a fractal butterfly antenna which can work in frequency band of 0.1~2 THz is designed. The proposed fractal butterfly antenna resonates at 0.6 THz frequency, and the minimum return loss can reach -15.89 dB and the maximum gain can reach 6.87 dB. The fractal butterfly antenna was optimized to generate a highly enhanced local field at the point of antenna. This highly concentrated energy coupling effect can effectively improve the performance of the terahertz detector.