The application of a steam injector to nuclear rectors as a water supply pump and a low pressure injection pump has been investigated. The heat transfer coefficient of the direct condensation of steam on the sub-cooled water surface which is indispensably required in designing and analytically examining the steam injector was studied in this research. A steam bubble was formed by ejecting steam from a 1mm diameter nozzle into sub-cooled stagnant water at atmospheric pressure. The measured heat transfer coefficient defined by temperature difference between the saturation temperature and liquid temperature and a time-averaged bubble surface area was much lower; approximately 1/100, than the realistic condensation heat transfer coefficient of steam. The measured value increased as the water sub-cooling increased on the contrary to that the realistic condensation heat transfer coefficient showed decreasing tendency with the sub-cooling increase. It was considered that when the steam bubble condensed in stagnant water, heat conduction in water provided large thermal resistance for the condensation.