The instability of metal electrodeposition will form dendritic crystals on the electrode surface. In high energy density zinc–nickel single flow batteries, dendrite formation is closely related to battery capacity and safety issues. Therefore, it is particularly important to explore the growth mechanism of dendritic crystals on the Zinc anode surface for inhibiting the growth of dendritic crystal and extending the service life of the battery. In this paper, the phase field-lattice Boltzmann method (PF-LBM) was used to establish the two-dimensional growth model of zinc dendrite to simulate the evolution process of zinc dendrite morphology and the temporal and spatial distribution of ions and electrons, and the influences of electrolyte flow rate, applied current density and anisotropic strength on the dendrite morphology were analyzed. The simulation results show that the morphology of dendrite can be changed and the formation of dendrite can be reduced by adjusting the anisotropy intensity. A larger electrolyte flow rate can not only reduce the ion concentration gradient on the cathode surface, but also increase the ion diffusion rate, making the current density on the anode surface more uniform, which could reduce the formation of crystal nucleus and slow the growth rate of crystal. A higher current density would increase the surface current inhomogeneity and promote the growth of dendrites.