InAs/GaAs and InAs/In xGa1-xAs/GaAs nanowire heterostructures are grown by metal organic chemical vapor deposition via Au-assistant vapor-liquid-solid mechanism. We find that the InAs nanowires grow directly on GaAs nanowires in a random way, or they grow along the sidewall of the GaAs nanowires, and thet InAs nanowires grow vertically on GaAs nanowires by using an In x Ga1-xAs (0≤x≤1) buffer segment. It can be concluded that the influences of crystal lattice mismatch and difference in interfacial energy can be eliminated by inserting a ternary compound semiconductor buffer segment, thereby improving the crystal quality and the capability to control the growth of nanowire heterostructure.