To simulate three dimensional (3D) solute-driven dendrite growth, a new numerical technique is introduced that combines the lattice Boltzmann (LB) and cellular automaton (CA) methods to calculate the transport phenomena and capture the solid/liquid interface, respectively. The effect of undercooling and degree of anisotropy on the kinetics of dendrite growth and the parallel performance of the model are studied. The present model can be used as a novel tool for simulating 3D dendrite growth with high computational efficiency and large-scale parallelization.