An experiment study of the dendrite growth of ice crystals growing in quiescent pure subcooled water was made at small subcoolings of 0.035 K < ${Delta}T$ < 1.000 K. It was observed that the growth kinetics and morphology are functions of not only subcooling but also thermal convection. When the subcooling is less than 0.35K, it was found that effect of thermal convection on growth kinetics of ice dendrites becomes important. Quantitiative measurements of growth velocity, $V_{G}$, and tip radii of the edge and basal planes, $R_{1}$ and $R_{2}$, were made simultaneously as a function of subcooling.