By resolving the characteristic equation of coated long-period fiber grating (LPFG), the dual peak resonant wavelengths is determined based on rigorous coupled-mode theory. The relationship between the dual-peak resonant wavelengths and grating period, the mode order is studied. The results show that the dual resonance appears in higher cladding mode. The higher the cladding mode order is, the smaller the related grating period required to couple with core mode is. Furthermore, the influence of film optical parameters and grating structure parameters on the intervals of dual-peak resonant wavelengths, as well as the attenuation peak of transmission spectra, are analyzed. The results are coincident with the non-coated long-period fiber grating experiment made by X. W. Shu. The research provides theoretical foundation for the structural optimization of dual-peak resonance film sensors with high sensitivity.