In this paper, we proposed a model coupling the lattice Boltzmann and the phase field methods with anisotropic effects is proposed, which is used to numerically describe the growth and movement of dendrites in rapid solidification of alloys. The model was applied to investigate the effects of dendrite movement and interfacial non-equilibrium on evolution of dendritic patterns for Si-9.0at%As and the CET for Al-3.0wt%Cu alloys. Both the growth and remelt processes of isolated dendrites are studied, and the result reveals the remelting influences on dendrite growth and solute micro-segregation in the condition of directional solidification. This dataset contains the underlying data for the above. This work demonstrates that the proposed model has a wide range of applicability and great potential to simulate the microstructure evolution with various solidification conditions.