We use plasma enhanced chemical vapor deposition (PECVD) to grow graphene with high quality and high transparency by setting the power of plasma generator and growth time to control the layer number of graphene. In the experiment, a fiber Bragg grating with a tilted angle of 8° is coated graphene with thickness of 3.7 nm (about 11 layers). Near the low refractive index region of 1.33, the titled-fiber Bragg grating (TFBG) has a high refractive index sensitivity of －1.57161 RIU-1, and its sensitivity is about 20 times of the sensitivity of TFBG without coating graphene. The way of coating graphene on TFBG can significantly increase the sensitivity of TFBG in the low refractive index region, and the TFBG coated graphene has potential application in the fields of biology, chemisty, food safety, and monitoring of water-environment.