A two-dimensional lattice Boltzmann-cellular automaton model is coupled with the CALPHAD (Calculation of Phase Diagrams) method for simulating dendritic growth during ternary alloy solidification with convection. In the model, the kinetics of dendritic growth is determined by the difference between the equilibrium liquidus temperature and the actual temperature at the solid/liquid interface, incorporating the effects of the interface curvature and the preferred dendritic growth orientation. The lattice Boltzmann method is used for evaluating the local liquid compositions of the two solutes impacted by diffusion and convection. Based on the local liquid compositions, the equilibrium liquidus temperature and the solid concentrations of the two solutes are obtained by the CALPHAD method. The model is applied to simulate dendritic growth of an Al-4?0 wt-%Cu-1?0 wt-%Mg ternary alloy with melt convection. The results demonstrate the high numerical convergence and stability, as well as computational efficiency, of the proposed model. Melt convection is found to influence the dendritic morphologies and microsegregation patterns in the solidification of ternary alloys.