We have demonstrated volumetric Bragg gratings (VBGs) for mid-IR spectral range based on LiF color center (LiF:CC) crystals. γ-irradiated LiF:CC crystals feature strong absorption bands in the visible and near-IR spectral range, where selective color center photo-bleaching allows for the LiF refractive index modification. The absence of active absorption in LiF:CC crystals at wavelengths longer than 1.3 μm results in a VBG that is stable under mid-IR irradiation. Our calculations predict a ~60% diffraction efficiency over 1-6 μm spectral range, which could be realized in a ~1 cm long VBG. To verify this, we fabricated periodic structures in LiF:CC crystals using an amplified femtosecond Ti:sapphire laser. Diffraction at 1.56 μm is demonstration of a phase grating in LiF and is a proof of the feasibility of LiF:CC crystals for mid-IR VBG applications.