To reveal the correlation between sound pressure and heat release rate of unsteady flames under oxy-fuel jet in cross flow. Correlation analysis of oxy-fuel jet in cross-flow on thermoacoutic instability flames was studied experimentally in a model gas turbine combustor. Four factors were investigated—the flow rate, temperature, injector numbers and injector diameters. Results indicate that thermoacoustic instability can be suppressed if the flow rate, injector numbers and the diameters of the jet in cross-flow increase. The average sound pressure amplitude declines from 23.6 Pa to a value that below 10 Pa. While thermoacoustic instability can be retriggered as the temperature of the jet in cross-flow increase. The correlation coefficient between sound pressure and CH* chemiluminescence under different CO2/O2 or N2/O2 jet in cross flow was presented. Correlation coefficients decline from 0.56 to zero as the flow rate or temperature increase, but it finally increases to a positive value. Correlation coefficients declines from 0.56 to zero as the injector number or diameter increase, but it declines to a negative value eventually. The length of flame fronts and roots was shortened as the flow rate or oxygen ratio increase. The average flame length declines from 110 mm to 70 mm. Three different flame modes were observed: the elongated root dominated, the shortened root dominated and the reattached dominated flames. This article could be instructive to the suppression of thermoacoutic instability in gas turbines.