Structural stabilities in GaAs nanocrystals grown on the Si (111) substrate have been studied by transmission electron microscopy in order to see the structure and growth mechanism. The GaAs nanocrystals grown epitaxially on the Si (111) surface kept at 573 K have thin shapes consisting of a flat surface which is parallel to the Si (111) surface. The crystalline structure of the initial growth layer, below approximately 5 nm in thickness is zincblend, but with increasing thickness the structure changes to the wurtzite structure by formation of orderly-arranged stacking faults. The small difference in the driving force between wurtzite and the zincblende structure could lead to a situation where the kinetic rate of nucleus formation is higher for the wurtzite structure than for the zincblende structure. It would highly increase the probability that the wurtzite structure is formed as a non-equilibrium state.