An anisotropic lattice Boltzman - phase field scheme is proposed to study dendritic growth in the presence of melt convection. In this work, the lattice Boltzmann method is extended to model dendritic growth with heat transfer and melt convection. It implements an anisotropic streaming-relaxation step based on the lattice Bhatnagar-Gross-Krook scheme. Three sets of distribution function are defined to describe the evolution of melt convection, heat transfer and phase transition. The D2Q9 lattice vectors are utilized to describe the advancement of ordering parameter, and coupled with a convective diffusion equation for heat transfer during phase transition. After model validation, dendritic growth with incoming flows and natural convection are numerically investigated, respectively. The results show that the present model is an alternative numerical approach to study convective dendritic growth with relatively high efficiency, and it would like to facilitate the understanding of microstructure evolution in solidification. (C) 2018 Published by Elsevier Ltd.