The III-V nanowire structure (zinc blende or wurtzite) grown by the vapor-liquid-solid process is shown to be highly dependent on the parameters which shape the droplet at the top of the nanowire. Under conditions that the droplet volume does not exceed a certain value, it is demonstrated that when the nucleation of the solid starts at the solid-liquid-vapor triple line, a relatively large droplet volume and low wetting angle favor the formation of the wurtzite structure. We show that the effective V/III flux ratio is the primary parameter controlling the structure.