The invention relates to a method and apparatus for safely producing hydrogen peroxide by injecting dispersed minute bubbles of hydrogen and oxygen into a rapidly flowing liquid medium. The minute bubbles are surrounded by the liquid medium of sufficient volume for preventing an explosive reaction between the hydrogen and oxygen. The liquid medium is formed of an acidic aqueous solution and a Group VIII metal catalyst. Hydrogen is sparged into the flowing medium for dissolution of the hydrogen in the medium. Oxygen bubbles are reacted with the dissolved hydrogen for producing hydrogen peroxide. Preferably, the liquid medium has a velocity of at least 10 feet per second for providing a bubbly flow regime in the reactor. The invention allows the direct combination of oxygen and hydrogen while preventing propagation of an explosive condition within the reactor. The method and apparatus provide for the safe production of hydrogen peroxide with low manufacturing costs.