The phase field model has emerged as a powerful tool for the simulation of crystal growth. With the thin-interface approximation, the interface thickness could be greatly relaxed to the length scale of microstructures. So far, the model is used only for linear kinetics. However, nonlinear kinetics, where the kinetic coefficient is a function of temperature or velocity, is often encountered in crystal growth, particularly for faceted growth. In this paper, we propose numerical methods to the thin-interface phase field model for nonlinear kinetics. Besides the benchmarking with the available solutions, an example on a facet growth that develops into different morphologies with different undercoolings is simulated for the first time. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.