We demonstrate a refractive index sensor based on a long period grating (LPG) inscribed in a special photosensitive microfiber with double-clad profile. The fiber is tapered gradually enough to ensure the adiabaticity of the fiber taper. In other words, the resulting insertion loss is sufficiently small. The boron and germanium co-doped inner cladding makes it suitable for inscribing gratings into its tapered form. The manner of wavelength shift for refractive indices (RIs) differs from conventional LPG, and the refractive index detection limit is 1.67 × 10⁻⁵.