A high-sensitive numerical measurement of methane based on the combined use of the localized surface plasmon resonance (LSPR) and Fano resonance in a slotted metal-dielectric-metal (MDM) periodic structure is numerically investigated. A groove is etched in an original MDM structure to excite the diploe mode at both sides of the groove, and the coherent coupling of two dipole modes is enhanced to realize a fast response, which is beneficial to gas-sensing. The influence of geometric parameters on the reflection spectra and methane sensitivity are analyzed to obtain optimal geometry. Moreover, an etching ring is introduced on the top metal to further raise the coupling area and coupling strength. The Fano resonance is subtly integrated into the optimized structure with asymmetry to achieve greater gas sensitivity. After the introduction of the Fano resonance, the field enhancement caused by the LSPR effect becomes greater and the methane sensitivity can reach up to 8.421 nm/% in numerical calculations, which increases 56.8% more than that of the original one. The combined use of the LSPR and Fano resonance in an optimized MDM structure provides an effective method for high-sensitive gas detection.