Based on coupled-mode theory, the eigenvalue equation of five-layered long-period fiber grating (LPFG) sensor with Ag film and gas-sensitive film overlays are firstly studied. The problem of resolving complex eigenvalue equation on five-layered LPFG is analyzed, and the method of resolution is also given. Then the eigenvalue equation of three-layered metal cladding LPFG is analyzed, and the complex transcendental equation is also discussed. The computing result shows that the coupling between the low-order EH modes and the core mode is much stronger than that between the low-order HE modes and the core mode.