A lattice Boltzmann (LB) based model is utilized to simulate three dimensional dendritic growth in directional solidification of alloys. The LB-D3Q19 lattice vectors are used to describe advancement of solid liquid interface, coupling with a conservation equation for solute transport in solidification. After model validation, the dendritic growth under several conditions of directional solidification was investigated and a solidification entropy was proposed to quantitatively characterize solidification morphologies. The results show that the present model captures tip-splitting occurring at a relative fast solidification rate. Initial thermal undercooling and solute concentration are dominant factors influencing the final microstructure. The solidification entropy reflects complexity of dendritic morphologies and it is useful to characterize dendritic growth in solidification. A design map was proposed to predict dendritic growth with and without tip-splitting, offering potential for simulating dendritic growth and microstructure evolution in solidification of alloys. (C) 2016 Elsevier Ltd. All rights reserved.