We investigate the size-effect on the surface tension of nano-scale gallium droplets by molecular dynamics simulations. The interaction among gallium metal atoms is described by a many-body potential. We derive a generic expression of the stress tensor to evaluate the surface tension of systems including many-body interactions. The equivalency between the mechanical and thermodynamic definitions of the surface tension is also proved in such systems. It is shown that the surface tension of gallium droplets increases with the droplet size approaching its value for a planar surface, which is consistent with the resent experimental result.