We present first fiber Bragg grating (FBG) inscribed in polarization maintaining (PM) optical fiber with artificially anisotropic core achieved by an appropriate distribution of discrete germanium-doped areas in nanoscale. We proved that this FBG reveals unique properties. Its single-resonance spectral shape, strain and temperature sensitivities are similar to that for grating written in cylindrically symmetrical optical fiber, which indicates that it behaves as the grating fabricated in a non-PM fiber, whereas it is written in the fiber that preserves the orthogonal polarization components of the mode. Moreover, due to the relatively low birefringence of the fiber, the FBG is insensitive to the excited polarization state and twist, and only a negligible shift of the spectrum is noticeable with no changes in its shape. Thus, FBG inscribed in ZEBRA fiber is a kind of hybrid structure that can be used for all-fiber lasers that generate polarized wave, as well as for polarization fiber sensors and components with spectral insensitivity to random or intentional twist.