We fabricated a multi-layer diffraction grating inside fused silica glass by using a femtosecond laser direct writing method. The femtosecond laser with a wavelength of 515 nm, a pulse width of 250 fs, a repetition rate of 100 kHz, and an average output power of 6 W was used. Two layer diffraction grating with a grating period of $6{mu}m$ was successfully fabricated with the layer gap of 0.5, 1, 2, 3, and $5{mu}m$, respectively. Also, we investigated the diffraction pattern by illuminating a He-Ne laser beam. Finally, we demonstrated the diffraction grating with a grating period of $3{mu}m$ by adjusting the gap of each layer with a grating period of $6{mu}m$. Femtosecond laser direct writing technology of multi-layer has a potential to fabricate the diffraction grating with a grating period of below $1.5{mu}m$.