The effects of air co-flow and equivalence ratio on flickering of a partially premixed flame of methane/air were experimentally studied for various combinations of burner diameters, fuel/co-flow velocities, and equivalence ratios of methane/air fuel. A scaling law was proposed by introducing the corrections made to the Froude number, equivalence ratio, and co-flow velocity ratio to describe the flickering characteristics of the flame in the co-flow. It is found that the corrected Strouhal number of the partially premixed flame increases with an increase in the co-flow at higher equivalence ratios with a frequency jump, whereas the value is still higher without the frequency jump at lower equivalence ratios. The oscillation amplitude weakens with an increase in the corrected co-flow velocity ratio at high equivalence ratios, which reduces at low equivalence ratios. The corrected critical co-flow velocity ratio used to suppress the flickering is found to be independent of the equivalence ratio in this scaling law. The proper orthogonal decomposition (POD) analysis of the flame indicates that the random flickering motion at high equivalence ratios is weakened and the fluctuating energy distribution of the lower POD modes is modified when the equivalence ratio is low. These changes in the flame structure are due to the disappearance of the clip-off flame in the partially premixed flickering flame at low equivalence ratios in the co-flow. (C) 2018 Elsevier Ltd. All rights reserved.