Pure oxygen combustion has been attempted with using a rapidly-mixed type tubular flame burner. Results show that tubular flame combustion can be obtained with oxygen molar concentrations of up to about 80% in the oxygen/nitrogen mixtures, above which very intense vibratory combustion occurs. Detailed observation shows that a diffusion flame is formed between the fuel and oxidant streams at the exits of the fuel slits, which prevents mixing fuel with oxygen, followed by violent turbulent combustion downstream the slits. Suppression of formation of the diffusion flame is indispensable for pure oxygen tubular flame combustion.