Thin-film lithium niobate (TFLN) modulators are expected to be an ideal solution to achieve a super-wide modulation bandwidth needed by the next-generation optical communication system. To improve the performance, especially to reduce the driving voltage, we have carried out a detailed design of the TFLN push-pull modulator by calculating 2D maps of the optical losses and Vπ for different ridge waveguide depths and electrode gaps. Afterwards the modulator with travelling wave electrodes was fabricated through i-line photolithography and then characterized. The measured Vπ for a modulator with 5-mm modulation arm length is 3.5 V, corresponding to voltage-length product of 1.75 V·cm, which is the lowest among similar modulators as far as we know. And the measured electro-optic response has a 3-dB bandwidth beyond 40 GHz, which is the limitation of our measurement capability. The detailed design, fabrication and measurement results are presented.