A new method to control the free spectral range of a long period fiber grating is proposed and theoretically analyzed. As the refractive index decreases radially outward in the silica cladding due to graded doping of fluorine, waveguide dispersion in the cladding modes was modified to result in the effective indices change and subsequently the phase matching conditions for coupling with the core mode in a long period fiber grating. Enlargement of the free spectral range in a long period fiber grating was theoretically confirmed.