In this paper, we demonstrate the buried waveguides directly writing in LiNbO3 crystal by a tightly focused femtosecond laser with repetition rate 75MHz, and the femtosecond laser was focused by the microscope objective of which NA is 0.65. Fabricating nine carved paths in LiNbO3 crystal by moving three-dimensional electric translation stage at different speeds varying from 2mm/s to 10mm/s, controlled by a computer. Analyzing the structure of the end face of the directly writing region by laser Raman, which shows the large-scale defects are generated in the center of the etching region, densification induced by the thermal effect of high repetition rate femtosecond laser interaction of LiNbO3 were generated below and down of the center of the etching region. Using a He-Ne laser focused by a microscope objective with NA 0.65 coupling to the end face of the prefabricated nine carved paths, which shows two waveguides are generated in the top and below of the inscribing region. Testing the insert loses of these waveguides with an optical power meter, the result shows that the insert loses of the waveguides fabricated at speed of 8~10mm/s is low to 3dB·cm-1, and the insert loses was low to 1.5 dB·cm-1 when the scanning speed is 9mm/s, moreover, the insert loses of the below region was low to the top region.