Because of the existence of anisotropic surface energy with respect to the hexagonal close-packed (hcp) lattice structure, magnesium alloy dendrite prefers to grow along certain crystallographic directions and exhibits a complex growth pattern. To disclose the underlying mechanism behind the three-dimensional (3-D) growth pattern of magnesium alloy dendrite, an anisotropy function was developed in light of the spherical harmonics and experimental findings. Relevant atomistic simulations based on density functional theory were then performed to determine the anisotropic surface energy along different crystallographic directions, and the corresponding anisotropic strength was quantified via the least-square regression. Results of phase field simulations showed that the proposed anisotropy function could satisfactorily describe the 3-D growth pattern of the α-Mg dendrite observed in the experiments. Our investigations shed great insight into understanding the pattern formation of the hcp magnesium alloy dendrite at an atomic level.