Long-period fiber gratings have been used for refractive index measurements under different conditions. Normally, this kind of sensor is based on measuring resonance wavelength shift with respect to different refractive index environments. As high order mode long period fiber gratings are attracting more attention, a new methodology based on intensity measurement of turning points is introduced, which involves simple experiment setup and straightforward demodulation process compared with wavelength shift based method. By using CO2 laser point by point irradiation method, high order mode gratings working at turning point can be easily fabricated. This type of grating has a very high sensitive response to surrounding refractive index, which can be used in chemical, medical and bio applications. In this paper, high sensitive refractive index sensor is demonstrated based on high order mode using intensity measurement. Phase match curve and couple mode theory are combined to analyze the intensity response to refractive index change at turning point of LPFG. This sensor is also demonstrated as an effective refractive index based glucose sensor with a range from 0 to 40 mM concentration of glucose solution, which can fulfill the medical requirement.