The dendritic growth of ice in supercooled water droplets is studied theoretically and experimentally. The measured dendritic growth velocity of ice shows a good agreement with the prediction of the Langer and Müller-Krumbhaar (LM-K) growth model at supercoolings less than 7 K, whereas an increasing overestimation in the latter is observed as the droplets are further supercooled. Therefore, the LM-K dendritic growth model is modified by considering the influence of interface kinetics. In the modified model, a dendrite grows in the limit of marginal stability coupled with diffusion at the liquid-solid interface, and the interface kinetics supercooling is introduced to predict the dendritic growth velocity. The interface kinetics factor is determined by fitting the experimental dendritic growth velocity within the framework of the modified model. This modification to the LM-K model well describes the dendritic growth of ice in water supercooled up to 25 K. It provides a solution to the dendritic growth of ice in the high-supercooling regime and can serve as a reliable input for studies on icing problems in engineering fields.