The lattice Boltzmann method on a face-centred hypercubic lattice has been extended by a phase-field model to calculate the interaction between the liquid-solid phase transition and the melt convection. The phase-field model is based on an analogy of chemical reactions and includes anisotropic effects of the growth. The method has been applied to a two-dimensional test problem: melting of Ga. Reasonable agreement has been found with the results of a state-of-the-art finite element calculation. The two-dimensional growth of a crystal with different growth rates in the <1 0 > and <1 1 > directions into an undercooled melt has been studied for different Stefan, Rayleigh, and Prandtl numbers.