A three-dimensional model is proposed to simulate the grain structure in directionally solidified silicon. This includes the nucleation and growth of grains in twin relationship whose formation is very frequent during silicon solidification. Based on analyses of in-situ and real-time observations of the crystallization front, a three-dimensional cellular automaton method is developed to model the dynamic of {111} facets, groove formation at grain boundaries, nucleation and growth of grains in twin relationship. The model is applied to well-characterized experiments assuming the frozen temperature approximation. A comparison of solidification sequences, crystallographic orientation maps, and coincidence site lattice maps in both experiment and simulation results is achieved. Results demonstrate that the model could be applied to optimize crystallization processes for both polycrystalline and cast-mono silicon fabrication processes.