A novel long- period fiber grating (LPFG) strain sensor is presented, which is based on dual- peak resonance combined with high sensitivity of LPFG nearby phase-matching turning point (PMTP). The dual-peak resonant characteristics near PMTP and strain sensing properties of LPFG are analyzed firstly by phase-matching condition of LPFG. It is found that dual-peak wavelength spacing has high response and linearity on small strain. Then, the influence of grating structure parameters and cladding diameters on sensitivity of dual-peak based LPFG is discussed and it is found that the grating periods affect the sensitivity, linearity and the range of strain. And the grating lengths have a valid influence on the peak and width,which directly concerns the precision of peek-peak. The results show that the sensitivity could effectively be improved by two orders of magnitude compared with that of the conventional LPFG strain sensor, if selecting the appropriate grating structure parameters and cladding radii. The research provides theoretical foundation for structural optimization of dual-peak resonant LPFG strain sensors with high sensitivity.