This study was focused on a flame structure of non-premixed flame which was stabilized in a fuel-air mixing layer. Especially, the variation of flame structure at near flammability limit was revealed with variation of fuel dilution ratio (FDR), fuel concentration gradient (FCG) and flow velocity. As a result, an interesting flame structure was observed; i.e., a diffusion flame branch was enclosed by two asymmetric premixed flame branches. Through the comparison of the structure of methane and propane, the unique flame structures near the combustion limit were discovered. The characteristic differences of them were discussed here.