This work aims to comprehensively study the solid-liquid coexistence phenomenon in Mg using the modified-embedded atom method (MEAM) in molecular dynamics (MD) simulations. We first employed the solid-liquid coexisting approach and predicted the melting point of 937.9 K, latent heat of 10.2 kJ/mol, and liquid density of 0.037 atom/Å3, which are in reasonable agreement with the experimental data. Then, the capillary fluctuation method (CFM) was used to determine the solid-liquid interface free energy and anisotropy parameters. To make the study more comprehensive, eight slip and twinning planes (basal, two prismatic, two pyramidal, and three twinning planes) are used as the solid-liquid interface planes. The average solid-liquid interface free energy of 122.2 mJ/m2 was predicted. The MD calculations predict primary dendrite growth direction of and a secondary dendrite growth direction of for Mg.