The influence of air co-flow on flickering methane diffusion flame was studied experimentally using the image processing technique and the proper orthogonal decomposition (POD) analysis. The flickering of the flame is characterized by the mean height, the oscillation amplitude and the Strouhal number, which are measured by the digital image analysis of the diffusion flame. The experiments are carried out for various combinations of burner diameters, fuel velocities and co-flow velocities. With increasing the velocity ratio of the co-flow to the fuel flow, the oscillation amplitude is decreased and the Strouhal number is increased slightly in proportional to the inverse Froude number, while the frequency jump occurs in the low co-flow velocity ratio. These results are commonly observed in all the burners of different diameters, while the critical co-flow velocity ratio to suppress the flickering is found to be increased with increasing the burner diameters due to the influence of Froude number. The POD analysis of the flickering flame shows that the flickering energy is dominant in the first two POD modes and they are axisymmetric except for the zero co-flow velocity case and fully suppressed case. The correlation of POD coefficients in the first two fluctuating POD modes suggests the suppression of large-scale structure of flickering due to the influence of co-flow.