A simple refractive index sensor based on a fat long period fiber grating (FLPFG) in a single-mode fiber is constructed and demonstrated. The sensor consists of periodical fattening region in a short piece of single-mode fiber. In this method, the fiber fattening is realized by applying a standard fusion splicing procedure on single mode optical fiber. The sensitivity of the sensor is 7.5 x 10-5 which the sensitivity is enhanced to the other kinds of long period fiber grating (LPFG).