We propose and experimentally demonstrate a method to significantly extend the sensitive window of tilted fiber-Bragg grating (TFBG) into low-refractive-index region with the integration of graphene coating. The coupling between cladding modes of TFBG and graphene coating results in an obvious modification of the cladding-mode envelope, which provides a sensitive regime relying on graphene's complex refractive index. Interacting the graphene-coated TFBG with various aqueous solutions, we observe strongly enhanced sensitivity in the low-refractive-index region of 1-1.428, which is about 10-fold extended from that of the unloaded TFBG. The graphene-coated TFBGs present great potentials in the biochemical sensing window.