In this paper a log-periodic terahertz antenna with metamaterial superstrate is proposed. A single-layer metamaterial structure, which utilized as a lens for the enhancement of gain of log-periodic terahertz antenna is used. The proposed metamaterial lens consist of an 8x8 matrix of Square Split-Ring Resonators (SRRs) and is placed above a probe-fed log-periodic terahertz antenna, resonating at 3.8 THz. The simulation result show that the proposed antenna achieves +9.991 dB gain at 4.521 THz, which is about +0.36 dB higher than the maximum gain of the conventional antenna. But proposed antenna provides a maximum gain enhancement of +1.11 dB at 3.846 THz frequency.