In recent years, the microfabrication of Lithium Niobate (LiNbO3) based optical integrated devices by using femtosecond laser pulses has been attracting increasing attention. One key current challenge is to understand the mechanism of the interaction of femtosecond laser pulses on LiNbO3 crystal, which is still elusive. Here we demonstrate the etching of LiNbO3 crystal surface by using tightly focused femtosecond laser pulses with repetition rate 75 MHz, pulse duration 50 fs, and single pulse energy 3nJ. The morphology of the etched area is observed by a scanning electron microscope (SEM) which shows the laser illuminated area has obvious thermal damage. When the etching time is 30 seconds and the etched area is 42μm in diameter, thermal damage is observed within the area with 28μm diameter, redeposition is observed in between 28-34μm diameter, and modification is observed in between 34-42μm diameter. A theoretical thermal diffusion model is built to simulate the temperature distribution in the area etched by laser pulses with repetition rates 1 kHz, 1 MHz, and 75 MHz, respectively. The simulation result from 75 MHz repetition rate matches experimental observation very well. The results show that there is thermal damage when LiNbO3 crystal is illuminated with high repetition rate femtosecond laser pulses.