Combustion instability has been widely reported in several combustion types; however, there is limited information on different fuel/air mixing distances in non-premixed combustion. Setting different distances between air tube and fuel tubes, the fuel/air mixing distances (δ) are changed by structural variations of nozzles. Keeping the heat load and equivalence ratios constant, the present work aims to examine the effects of fuel/air mixing distances on combustion instability in non-premixed combustion. Experimental observations suggest that combustion oscillations occur in non-premixed combustion with flame ignited outside the nozzle rather than other types of non-premixed combustion. Quasiperiodic oscillations, limit cycle modes, and intermittency modes are found in three fuel/air mixing distances in non-premixed combustion. The calculation methods of convection time for non-premixed combustion are established in the present work. The convection time of the limit cycle oscillations is then calculated, which is further found to trigger the second resonance modes of the combustion system. The further analysis reveals that varying fuel/air mixing distances can cause influences on local equivalence ratio distributions, and the convection time are correspondingly varied. The changes in convection time affects the coupling characteristics between heat release rate fluctuations and the acoustic modes in the combustion chamber. When the thermoacoustic coupling occurs, combustion instabilities appear. This work establishes a link between combustion instability and fuel/air mixing distances in non-premixed combustion and highlights the influences on spatial distributions of local equivalence ratios and then convection time, which can provide technical guidance for actual applications in various fuel/air mixing types.