This work presents a refractive index sensor based on a long period fiber grating (LPFG) made in a reduced cladding fiber whose low order cladding modes have the turning point at large wavelengths. The combination of these parameters results in an improved sensitivity of 8734 nm/refractive index unit (RIU) for the LP0,3 mode in the 1400-1650 wavelength range. This value is similar to that obtained with thin-film coated LPFGs, which permits to avoid the coating deposition step. The numerical simulations are in agreement with the experimental results.