Highly sensitive refractive index sensing is realized by using dual-peak resonance long-period fiber grating (LPFG) with self-assembled coating. The way for improving the sensitivity of coated dual-peak resonance fiber gratings to the surrounding refractive index is given. The fiber cladding mode is located near the mode transition zone by choosing optimal film thickness. The dual-peak structure of fiber coated is located near phase-matching turning point (PMTP) by adjusting the fiber radius. The method for determining optimal film thickness and fiber radius is given. Dual-peak gratings with different fiber radii coated with poly allylaminehydrochliride (PAH)/ poly acrylic acid (PAA) films are immersed in different concentrations of glucose solution to carry out refractive index sensing experiments. Results show that the sensitivity of coated dual-peak gratings operating near mode-transition regions and PMTP is 3985 nm/RIU in 1.333~1.372 index range, which is obviously higher than those of gratings not operating near mode-transition or PMTP, and also higher than that of non-dual-peak coated LPFGs reported.