Phase change accompanying conversion of a saturated or superheated vapor in the presence of subcooled surfaces is one of the most common occurring phenomena in nature. The mode of phase change that follows such a transformation is dependent upon surface properties such as contact angle and thermodynamic conditions of the system. In present studies, an experimental approach is used to study the physics behind droplet growth on a partially wet surface. Superheated vapor at low pressures of 4-5 Torr was condensed on subcooled silicon surface with a static contact angle of 60 degrees in the absence of noncondensable gases, and the condensation process was monitored using environmental scanning electron microscopy (ES) with sub-microscopic spatial resolution. The condensation process was analyzed in the form of size growth of isolated droplets before a coalescence event ended the regime of single droplet growth. Droplet growth obtained as it function of time reveals that the rate of growth decreases as the droplet increases in size. This behavior is indicative of an overall droplet growth law existing over larger time scales for which the current observations in their brief time intervals could he fitted. A theoretical model based on kinetic theory further support the experimental observations indicating a mechanism where growth occurs by interfacial mass transport directly on condensing droplet surface. Evidence was also found that establishes the presence of sub-microscopic droplets nucleating and growing between microscopic droplets for the partially wetting case.