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We propose a newly designed X-cut lithium niobate (LiNbO3) optical modulator. It has a two-step back-slot structure to satisfy the velocity-matching condition without the buffer layer of silicon dioxide (SiO2). Accordingly, this modulator can achieve low drive voltage and low optical insertion loss. In addition, the dc-drift phenomena due to the buffer layer can be suppressed. This structure is fabricated with micromachining technology using excimer laser ablation. The optical 3-dB bandwidth of the fabricated modulator reaches 30 GHz, and the drive voltage is less than 3 V at 1 kHz. From the measurement of the optical eye diagram at 43.5-Gb/s, clear eye openings were obtained. This modulator is sufficient for 40-Gb/s optical transmission systems.