In this study, a multi-jet burner with an extremely intense flame was designed for oxy-fuel combustion. The flame characteristics were experimentally and numerically investigated at a fixed overall flow rate of fuel and oxygen and at oxygen feeding ratios (OFRs) of 0.25, 0.5, and 0.75, which gives an overall equivalence ratio of 0.909. The measured temperature profiles were compared to values predicted by numerical simulations, and good agreement was observed. To determine the cause of differing flame height at various OFRs, the iso-surfaces of the fuel, oxygen mole fraction, and the mixture fraction in the physical space were investigated using the numerical data. These results can be understood through an analysis of the scalar dissipation rate, which signifies the mixing characteristics of the fuel with the oxygen and the destruction of scalar fluctuations by turbulent mixing. The flame height seen at an OFR of 0.25 was the lowest because the peak scalar dissipation rate was higher than at other flow conditions. This information is important to reduce the flame height for the control of an intense flame.