Currently, a majority of Volumetric Bragg gratings (VBG) use photorefractive glasses with a transmission band between 0.3 and 2.7 μm. We have proposed and realized VBGs for mid-IR spectral range based on LiF color center crystals (LiF:CC). 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:CCs at wavelengths longer than 1.3 μm results in a VBG that is stable under mid-IR irradiation. Our calculations predict that ~60% diffraction efficiency over 1-6 μm spectral range could be realized in ~1 cm long VBG. To verify this calculation, we fabricated periodic structures in LiF:CC crystals with 24 and 12 μm spacings by CCs photo-bleaching using femtosecond Ti:sapphire laser pulses. Periodic structures exhibit diffraction in multiple orders in the Raman-Nath regime at 0.532, 0.632, and 1.56 μm. The first order diffraction efficiencies were stronger for a visible radiation due to a bigger refractive index variations and additional amplitude modulation. The demonstrated diffraction at 1.56 μm is a clear manifestation of a phase grating in LiF and serves as a proof of feasibility of these LiF:CC crystals for mid-IR VBG applications.