Explosion hazards associated with hydrogen-oxygen mixtures remain a significant challenge for the energy industry, despite hydrogen garnering attention as a carbon emissions-free alternative energy source. While several studies have been conducted on hydrogen-air explosions, research on hydrogen-oxygen explosions has been limited. In the current study, we employed a spherical soap bubble method to experimentally investigate the flame propagation behavior of an unconfined hydrogen-oxygen explosion. The experimental values of the laminar burning velocity were in agreement with its calculated values and were notably higher than those observed hydrogen-air mixtures. In the case of hydrogen-oxygen mixtures, a spherical expanding flame is accelerated due to the presence of Darrieus-Landau and diffusive-thermal instabilities. Furthermore, we compared the correlation between the critical Pѐclet number and the critical Karlovitz number with the Markstein number for hydrogen-oxygen mixtures to results obtained with propane-oxygen and methane-oxygen mixtures.