A phase-field lattice-Boltzmann method coupled with the parallel-adaptive mesh refinement algorithm is developed to simulate the equiaxed and columnar dendritic growth of hcp metal alloys. The effect of gravity-driven natural convection on the dendritic growth is discussed separately and also coupled with forced convection. The simulated results show the asymmetric dendritic growth of hcp metal alloys in two dimensions under gravity-driven natural convection, and reveal the evolution process of solute segregation and solute plumes. It can be concluded that the solute plume formation is determined by the competition between the solute blocking of dendrites and solute transport of the melt flow. Introducing an appropriate forced convection can eliminate the solute plume formation and dampen the local fluctuation of solute concentration in front of the dendrite tips. It is also found that the gravity-driven natural convection enriches the diversity of the 3D dendritic morphology of hcp metal alloys.