The development of grain structures during directional solidification of multi-crystalline silicon (mc-Si) plays a crucial role in the materials quality for silicon solar cells. Three dimensional (3D) modelling of the grain boundary (GB) interaction and evolution based on phase fields by considering anisotropic GB energy and mobility for me-Si has been developed recently. Here, we further consider twin nucleation at the tri-junction groove for the simulation. To compare with the experimental results, the initial seed orientations are described by the Euler angles. With the previous developed twinning model at the three-grain tri-junction and the T matrix for twinning, the simulated grain orientation and the resulted GB types are consistent with the experiments.