Laser-induced breakdown spectroscopy (LIBS) has been increasingly used in combustion diagnostics as a novel spectral analysis method in recent years. The quantitative local equivalence ratio of methane/air mixture is determined by LIBS using different emission intensity ratios of H/O and H/N. The comparison between calibration curves of H₆₅₆/O₇₇₇ and H₆₅₆/N₇₄₆ is performed in gated mode, which shows that H₆₅₆/O₇₇₇ can achieve better prediction accuracy and higher sensitivity. More spectral intensity ratios (H₆₅₆/O₇₇₇, H₆₅₆/N₅₀₀⁺, H₆₅₆/N₅₆₇ and H₆₅₆/N₇₄₆) can be used to make calibration measurements in ungated mode and H₆₅₆/O₇₇₇ is also tested best among them. The comparison between gated and ungated detection modes shows that gated mode offers better accuracy and precision. In addition, the effects of different laser wavelengths (1064, 532 and 355 nm) on LIBS spectra and calibration curves are investigated with laser focal point size and laser fluence kept constant. The results show that with longer laser wavelength, the peak intensity and SNR of H, O and N lines increase, as well as the slope of calibration curve of H₆₅₆/O₇₇₇. Among these three wavelengths, 1064 nm laser is best suited to measure the equivalence ratio of CH₄/air mixture by LIBS. The experimental results are explained in terms of plasma electron density and temperature, which have a significant impact on the emission intensity and the partition function of hydrogen and oxygen, respectively.