The effect of equivalence ratio and velocity on the stability of flame in dump combustor was studied in an atmospheric pressure, laboratory scathe dump combustor operating natural gas. Traditionally, peak-to-peak pressure, fluctuation of the heat release rate and Rayleigh index were used to find and control the combustion instability. Cross correlation coefficients, Ci,j which is defined as the normalized value of the integration of the product of two of the mixer pressure, dump plane pressure and heat release rate, are introduced to see whether the flame is stable or not. Ci,j shows more sensitive to combustion status than Rayleigh index in steadily burning flame. Also, the result indicates that the amplitude of Ci,j between heat release and mixer pressure goes up before the flame at the rich de-stabilizing equivalence ratio near $psi$=0.85. t means Ci:j at this case has a potential to detect the de-stablizing moment in prior to becoming unstable in dump combustor.