Laser-induced breakdown spectroscopy (LIBS) has been applied to both non-reacting and reacting opposed jet flows to evaluate the measurement accuracy of instantaneous, local air-fuel ratio. However, the LIBS signal is much weaker in flames than in the corresponding non-reacting gases and more work is required to investigate the potential of this technique for instantaneous measurements in reacting flows and quantify measurement uncertainties. The present study reported local equivalence ratio measurements of methane/air flames in an opposed-jet burner, which allowed independent control of flow rate and air-fuel ratio. Images and emission spectra of laser-induced plasma were investigated simultaneously using both an Intensified CCD (ICCD) and a spectrometer with a high degree of spatial and temporal resolution. The influences of the camera delay time, exposure time and laser pulse energy on the LIBS measurements were investigated as well. The dependence of spectral intensity ratios of H/O and C2/CN on air-fuel ratio was quantified over a wide range of conditions extending from pure air to pure fuel. It was found that H/O and C2/CN intensity ratios depend monotonically on the mole fraction of methane in the ranges of 0.0-0.8 and 0.3-1.0 respectively. The presence of a flame within the laser beam led to significant measurement deterioration relative to the corresponding non-reacting flows. This could lead to increased measurement uncertainty, and was therefore corrected by increasing the laser pulse energy and applying a proposed data processing method; the proposed correction method was able to reduce the equivalence ratio measurement uncertainty to be within 10% for mixtures with methane mole fractions lower than 50% and within 15% for mixtures with higher methane mole fraction. The established correlations between the intensity ratios of H/O and C2/CN with local air-fuel ratio allowed measurement of the spatial gradient of air-fuel ratio across opposed jet diffusion flames. The LIBS measurements of air-fuel ratio in non-premixed flames were finally compared successfully with CHEMKIN simulations, which demonstrates the ability of LIBS to accurately measure the spatial gradient of the air-fuel ratio.