Density change is ubiquitous in phase transformation, and it can induce melt convection which strongly influences the crystal growth. Here, an anisotropic lattice Boltzmann-phase-field method was extended to predict the dendritic growth under the shrinkage or expansion melt convection by density change induced. A novel LB equation with an anisotropic coefficient was constructed to model the advancement of ordering parameter, coupling with the passive scalar LB equation for convective and diffusive heat transfer during phase transition. We studied dendritic growth and shape selection with melt convection induced by density change in crystal growth. Results show that the melt convection induced by density change affects strongly the dendritic growth. The shrinkage flow results in a higher tip velocity while the expansion flow leads to a slower one. Predicted Peclet number with respect to the relative density change was compared with an analytical solution. Moreover, the modified selection parameter has been verified by numerical simulations. (C) 2020 Published by Elsevier Ltd on behalf of The editorial office of Journal of Materials Science & Technology.