A great challenge in the Simulation of dendritic crystal growth from various supercoolings is the large difference in time and length scales. Using adaptive mesh refinement and rescaling, we show that an efficient phase-field simulation for dendritic crystal growth at various supercoolings is feasible. our simulation results are in good agreement with the experiments and classic solutions. The rescaled tip radius and speed are independent of supercooling. The dendrite tip shape is also in a self-similar manner for a wide range of supercoolings. (c) 2008 Elsevier B.V. All rights reserved.