ZnO nanotetrapods and nanorods have been synthesized by a simple thermal evaporation of Zn powder (300 mesh, 99.99% purity) under simultaneous flow of oxygen and argon gases in two-zone furnace in two different temperature regions. These ZnO nanostructures have hexagonal structure, which grow along the [001] direction in the form of nanotetrapods (diameter approximately 60-150 nm, length approximately 1-4 microm) and nanorods (diameter approximately 30-60 nm, length approximately 2-5 microm). The morphologies of these ZnO nanostructures have been investigated by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). It has been found that growth parameters like temperature, gas flow rate etc., control the diameter of the nanotetrapods and nanorods. These novel structures of ZnO nanorods and nanotetrapods may be attractive for optical and other nanodevices.