To investigate the fundamentals of liquid oxygen droplet combustion in hydrogen under microgravity conditions, a drop tower apparatus has been developed. In a cryogenic combustion chamber cooled with liquid nitrogen, single oxygen droplets with a diameter of 1 mm are suspended at the tip of a thin suspender. Ignition is accomplished after microgravity conditions are reached by a near-infrared laser, which generates a plasma spark positioned in the immediate vicinity of the oxygen droplet. The subsequent combustion is investigated with various optical diagnostics. Shadowgraph imaging is used to determine the initial droplet size and the droplet diameter regression with high temporal resolution. In addition, the position and diameter of the flame are determined by OH chemiluminescence imaging. The oxygen/hydrogen combustion at two different pressure levels is reported. At a pressure of 0.1 MPa, irregular structures appear to form on the droplet surface during the combustion process, which lasts 137 ms before the droplet is completely consumed. The formation of these irregular structures is consistent with the condensation and freezing of water vapor in the cold-temperature region near the droplet surface. At a higher pressure of 4 MPa (reduced pressure pr,O2 = 0.79), the water ice formation is significantly reduced due to the shorter burning time of 66 ms and the closer proximity of the flame to the droplet surface. The measured burning constant is k0.1 = 5.5 mm2/s at 0.1 MPa and k4 = 7.1 mm2/s at 4 MPa, respectively. This increase with increasing pressure is consistent with the smaller flame standoff distance.